It's sad that you think it is begging. I think if it as patronage, something that is baked right into the name of the service.

begging implies some kind of charity. Patreon is enabling one exchange of value for another. Very different IMO.

Producing content is never free. (if not in monetary cost, then in time/opportunity cost)

It is not "begging" so to speak; if anything, it's a win-win.

I wish I could get my head around this, I'm an artist and people tell me my work is good and I do sell some, but I can't bring myself to go on to Patreon because I feel like it's begging (although weirdly I only apply this to myself, I don't think badly of other people that do it... but then I don't look down on people who beg anyway, I grok St. Francis of Assisi so I'm not sure what all of this means). Meanwhile I've moved into a caravan and often have trouble affording to eat (luckily I'm still a bit fat haha).

Everyone has to sell. They're not "begging", they're offering a service: I keep doing art. That's a pretty good service to me.

A little, but people using these tip sites are generally in an awkward spot. They make content that lots of people enjoy but it's not valuable enough that people would directly pay for it. The opportunity costs of actually paying quickly eclipse the value of the content so people choose to do without. It's the same situation with a lot of paid apps.

Of the two, beg (a.k.a. ask) for money is preferable - it's more direct and more relevant. Imagine showing up to your job and the only way to get paid was to sell ads to some other third company and show the ads to your employer. The ad model has needed a good "disrupting" for a long time...

Its not begging, it's capitalism.