Phone numbers in the US: Presumably, when the current system overflows available capacity for numbers, we will simply add additional numbers. This used to be a difficult solution with mechanical switching devices, but now that the phone companies are (essentially) all digitalized, that just means a programming change. Probably, they are working on it right now and someone with knowledge of that will show up shortly to say what the proposed solution is.
As to California license plates on cars: There are practical limitations on how many digits you can have on the plate and still have it be readible. However, there is no reason that they cannot move the location of the numbers and letters around. That’s what they did back in about 1970, when they switched the letters and the numbers (used to be LLL NNN, but became NNN LLL, while also switching the color from gold on black to gold on blue). They then ran out of NNN LLL, so they went to the current seven-character system of NLLLNNN. So there isn’t any reason they couldn’t do LNLLNNN, followed by LLNLNNN, etc., and still use only seven characters.
Silenus, there is nothing at that link to suggest they wouldn’t run out of available plates using NLLLNNN. Indeed, since they are already up in the 6LLLNNN range, possibly even the 7’s by now (I think my recent rental was a 6ZLLNNN plate), it’s surely forseeable that they will need to change the system soon.