Not sure that tells me a lot - I pronounce the vowel sounds in cot, bother, and father exactly the same, but “caught” is completely different.
In my experience (51 years as a Texan), the bother/father distinction is more contained in the Northeast US, but in the rest of the country they’re the same sound. The cot/caught distinction is most of the US except the West coast. I have no doubt people will jump in here and let me know where I’m off.
Yeah, I don’t know what I was writing there. I really meant to say it’s generally not done. I can think of many artists that do it, but it’s one of those things that a classical vocal coach would be aghast to hear.
I still have issue with the word ‘lazy’, but I’ll let it glide. 
Although imo - There isn’t really anything easier, or harder about not including an intrusive r, or using a diphthong or whatever it is you’re going to do when hiatus occurs. It all depends on what you’re used to. And - (even if it was more difficult) I don’t think making language harder for yourself is necessarily a commendable thing.
I imagine it depends on what the voice actor is doing though. If it’s fictional dialogue, then it will want to sound like real conversation.
This is an interesting one though - I personally find the ‘intrusive r’ to sound a lot better than using a diphthong or inserting a noticeable pause. Maybe that’s because I live in the UK and I’ve grown up hearing it pretty much everywhere.
To an American, most Brits seem to treat R as a semi-vowel that melds completely into the leading vowel sound whereas most (not all) Americans enunciate (rhoticize) it most of the time. Hence, in American English, “father” expresses three consonants whilst “farther” expresses four; from British English, Americans will tend to hear only two consonants in both of those words.
As seen in that American movie, The Horace Whisperer. 
I know what the difference is, in theory, and I can see that the IPA transcriptions are different, but those two clips sound exactly the same to me.
And to me, and I’m a native British speaker. My point was, there is no difference in RP.
I can say “tuna oil” while maintining voicing with the “intrusive R” but it requires a little more deliberate control of mouth/tongue.
To most Americans, it just sounds wrong.
Imagine if you heard a dialect where someone inserted an “L” sound between a word that ended in a vowel, and another beginning with a vowel. So instead of saying “Asia and India,” they said “Asial and India.” You’d say “WTF’s up with that? You put an ‘L’ sound in there where it didn’t belong!” and the person said “No, I didn’t!” That’s what this conversation is like to an American.
I guess I would say, WRT this vowel separation issue, American English tends to be violinesque, gliding smoothly from sound to sound the way a C# would flow into a G when that horizontal parenthesis thing connects them (continuous bow stroke). The RP is more lutish, plucking out the words as distinct notes.
For instance, when I say “Data and I”, there is a change in the vowel sound, so I just do something not unlike a note glissando thing. But if I were to say “I see Eden”, you might not even be able to find the word boundary because those are identical sounds. The same thing sometimes happens with matched consonants: “I can’t talk” can seem indistinguishable from “I can talk” except the emphasis is in “can’t” in the former, “talk” in the latter.
Perhaps American English is more tonal than RP, relying heavily on the musical structure of the spoken language for clarity? I know that I have uttered sentences that were incredibly muddy, nearly unintelligible, but the listener was able to understand me almost wholly by tone.
Funny example–surely with the intrusive ‘r’ the above becomes a complete tongue twister?!
My dialect matches yours on all of those points. What’s your origin? Mine’s Northern Ohio.
Mine also matches those, and I’m Chicago. Which would make sense, as at least parts of Northern Ohio (Cleveland, I’m thinking in particular) has a similar accent: the Great Lakes accent (or whatever it’s called.)
To those of us with the cot/caught merger, they are the same sound. Sure, they are written differently, but so is “two” and “to” and “too”. Or “sea” and “see”.
It’s kinda like the schwa (uh) - all the vowels get muddied into one pronunciation.
I would tend to pronounce your name “Colofahn”. Sounding like “telethon”, not “telephone”.
I know a guy from the hill country, named Brian - “Briiiine”. (Draw out the “i”, leave out the “a”.)
To those of us who hear these vowels the same, you are speaking gibberish. “That’s like the difference between sea and see.” 
When you write it out, we cannot hear the difference you are trying to make. We read the words in our own dialect, and hear the sounds the way we sound them - the same.
From tends to be “frum”.
For me, caught has a slight variance from cot, but it is very tiny.
Cot is simple, short one vowel. Caught has the slightest amount of “w”, but the rest of the vowel is the same. Try saying “cot” but just slightly bowing the lower lip inward just before the “t”. It’s very subtle, and I can imagine some people not hearing it, especially if the words aren’t back to back. And they usually aren’t.
Can you give an example that doesn’t use an “r”? Because rhotic r dwarfs any vowel sound difference.
For the cot/caught links you gave, I hear
cot = cot
caught = cowte (almost coat, with a little more w).
Yeah, describing sounds is hard.
Listen to the American father and American cot
and just for grins
Yep, Cleveland, precisely. Born & bred.
Pasta.
Please don’t tell me you rhyme pasta with “faster”
I had an Australian friend who rhymed “rear” and “idea” in a message board game. Later, I met him in real life and he explained it, and the way he said “rear” was like “rea.”
And I’m a hick from the piney woods of East Texas.
“Pass” has the same vowel as “father” in my southern English accent, as do “bath”, “calm” and “raft”. In a northern accent, “calm” and “father” would probably still have the same vowel, similar to mine (I don’t have a northerner on hand to check) whereas “bath” and “raft” would have a shorter vowel, as in “hat” or “batter”.
What I was trying to point out that, for example, was that Mary, Merry, Marry have different vowels and consonant counts and so in British, Australian, New Zealand, South African, Indian & Singaporean English, will be pronounced differently to each other.
The fact that they are pronounced the same to you, is a matter of your local accent.
The pronunciation of those words will have regional/national variations in pronunciation in the rest of the world, but will most likely still maintain some distinction that another person will identify the word being said if it were said in isolation.
I wasn’t using the term “lazy” in a perjorative way. I speak the same way at times.
Just “experimenting” with the “tuna oil” again, and the difference is so slight in tongue positioning for the glide. Maybe I am too conscious of it now, but the non intrusive version is not so difficult but it’s easy to slip in an “intrusive R” without thinking.
As you suggest, it’s not offensive, we’re used to it in Australia, UK, NZ and so on.
My original point is that it’s not a DELIBERATE insertion of an “R” sound which the term implies !
As for the voice actor thing, I was referring to professional voice talent, the type you hear on TV commercials or documentary narrations, so it’s not the same as you’d hear with an actor playing a fictional character.
Just think of the difference between Andrew Sachs narrating a doco versus Manuel in Fawlty Towers !!
Same with an Australian accent. For our American friends the sound may differ between Colophon’s Southern English accent, and an Australian accent, but the consistency of the vowel across those words will be similar.
Also agreed, those pronunciations of “bath” and “raft” are recognised as being regional variations of British speech.