Raising Hope and My Name is Earl were created by the same guy (Gregory Thomas Garcia) - and he apparently likes working with particular actors. Joss Whedon has favorite actors too - so if you see them on Angel, you’ll see them on Buffy, or Firefly too.
TLDR - it’s not the actors who advocate for their friends - it’s the producers/showrunners who choose to work with particular actors on more than one project.
Some directors seek out actors they enjoy working with. Quentin Tarantino, for example has directed Samuel L Jackson in Pulp Fiction (1994), Jackie Brown (1997), Kill Bill: Volume 2 (2004), Inglourious Basterds (2009, uncredited), Django Unchained (2012), and The Hateful Eight (2015).
It’s very common for producers or directors to have a cabal of actors that they really enjoy working with. You’ll find a lot of the same people keep popping up in stuff by the Coen Brothers, Kevin Smith, Michael Schur, Wes Anderson, etc.
It goes back a long way. Director/Producer John Ford had a “stock company” of actors he used over and over. It boiled down to the fact the Ford liked what they brought to a film.
The Three Stooges worked with Emil Sitka, Bud Jameson, and Vernon Dent dozens of times.
Even earlier, Charlie Chaplin worked with Edna Purviance and Eric Campbell in many of his short subjects.
There are some married couples who frequently get cast together or even produce their own projects in which they work together, like Michael Tucker and Jill Eikenberry.
It’s not different from any other industry. Most of us work in jobs where we don’t have the luxury of working with our friends. But if you have the money and the liberty to do so, who wouldn’t want to work with their buddies? In a creative industry, I suspect it is especially important to work with like-minded people you can count on. How often do you hear about people leaving or being fired from a production because of ‘creative differences?’
Tim Burton is very fond of working with Johnny Depp and with Helena Bonham-Carter, and the trio can be found together in the credits of quite a few movies.
A number of people have correctly mentioned that producers often have a stable of actors they like working with.
But another factor is stunt casting. The hope is that audiences will watch a pairing of actors that they have watched working together in previous productions. Kevin James, for example, worked with Leah Remini on The King of Queens for several years and it was a popular show. A few years later, James has the lead in another sitcom, Kevin Can Wait. When the ratings on that show were low, the producers cast Remini as a regular in an attempt to increase its popularity.
I would also assume it has a strong business side to it besides “they like working with them.” Everything about a movie cost money. Time and mistakes cost money.
You are the director. You can go with an completely unknown, but you may have to do more casting calls. You select a person and you think they will work out but…maybe not. Or you can go with an actor that you don’t know well, but maybe they will be difficult to work with.
If you go with a known quantity, that saves money all around. No restarts because the unknown actor’s talent wasn’t quite up to snuff. No restarts halfway through the production because the lead actor and the director got in a fistfight.
That’s not really stunt casting though. Stunt casting is more for guest shots, not introducing a new primary character. So when Ed O’Neill played Katy Sagal’s old high school boyfriend on “Eight Simple Rules”, or half the cast of Cheers showed up on “Becker.”