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I've pointed out a number of times the similarities between stand-up comics and other self-employed solo operators. Things like a need for personal branding, understanding that you're really only being as good as your last job and being able to deal with career vicissitudes on your own. There are blatantly obvious differences in that most people would see a career of telling jokes to random strangers as a version of hell.
A less obvious difference is the end-point of all the effort. Most self-employed people I know want to achieve little more than a level of financial well-being without having a boss, whereas every comic wants to be famous.
This means that most self-employed people are only ever rivals when in a competitive pitch; occasionally if ever at all. The rest of the time we're just people trying to pay the mortgage who happen not to have to book their holiday time months in advance. There's plenty of room for everyone.
In UK there are maybe 30 genuinely famous working comedians. By famous I mean well-known enough to get stopped on the High Street. They are all on television. And they are the envy of hundreds and hundreds of other comics.
Because it has such a specific definition, a field like 'UK stand-up' will inevitably disappoint the vast number of players who enter it. Something as vague as 'being self-employed' has room for many more success stories.
You can do better than seeing 'paying the mortgage' as being in any way remarkable. What do you really want to achieve?