The level of income should always impact the speed of development. Its literally the whole economy of gaming. The more money you have the bigger your team can be and the more products you can release to the market. When games face delays it usually comes down to the development team, circumstances with the direction/director or last minute publisher demands. As you mentioned that he is indie and has no one warping his vision to add microtranctions for example, then thats not a liable excuse. You cannot tell me that a developer who is making over half a million a year cannot bring in other people to work on Renpy code. This is not rendered in the Unreal engine with high end 3D graphis. It is simply an image based game. It should never take six months for an update when you have that level of income coming in. Renpy code is much easier. I know that he does his own art which is a step above a lot of the prerendered 3D art that is use by other developers. And in fact I would say that his game is one of the best one out there compared to the competition. However I always go back to $50K a month, $300K in 6 months is not enough to release an update? If that is the case it is time to bring some more people into the team. But I do see your points.
While, in general, budget dictates release speeds, it's not the rule. Especially on a free for everyone title where you're not paying for access. His patrons are, primarily, paying him for two reasons:
1. People like what he's done so far, so they are tipping him an average of $3 a month.
2. People like what he's done so far, so they're investing an average of $3 a month for him to continue developing.
Very few people are actually complaining about his update speeds. He has over 17,000 patrons and most are pretty quiet. Some few are complaining but they're the minority. If I'm not mistaken, he even had a poll about updates and the majority voted that how it was progressing was fine. Most people would rather have higher quality content, even if that means waiting a while.
Skip to next paragraph if you don't wanna read this- As for the actual income, no one can speak for that except DC and his financial people (if he has any). It's not like he gets 50k free and clear. Patreon takes their cut and then you start going into taxes and whatnot. Income tax, possibly business taxes since he, technically, is a business now, etc. He also has six staff (according to the Team page for Kompass Productions) working on the game that gets paid from that 50k. I don't know how that's split but if it was an even split, he'd be bringing in over 7k a month before taxes. Less because Patreon takes a 5% cut of that IIRC. Based on the United States tax brackets, and him making around 84k a year, he's looking at 22% tax rate, so that's around 65k a year after taxes.
Regardless, of my rambling, I'm just saying it's not as easy as just looking at the base amount he's making and assuming it all goes into the game. These people have spouses and children and some work full-time on the game. It is their job, it is their sole source of income, so some of that money goes to everyday living costs.