Small popular programs get extended, grow, are improved by large teams of paid programmers, and then eventually the category becomes so advanced that you need to have that large team to make progress. I can (and have) written Tetris in 3-4 hours, but there's no way I could write Starcraft 2. But that doesn't mean that small programs have become impossible to write; it just means that you have to start looking where other people are not. Look at the success of 2048 or Flappy Bird. There's probably another category-killer out there for small-business apps, but if someone's found it they aren't going to advertise it.
A friend of mine used to refer to it as cowboy engineering - where a problem needs to be solved yesterday, and everyone does anything necessary to solve it. Nowadays, even on side projects, the overhead kills you - issue tracking, version management, module management, change tracking, support. Precious little time ends up being spent on the core problem in most jobs.
> it just feels like one programmer can't make any impact any more
Can you explain in more detail what makes you believe this?
Some of the most creative solutions redefine the problem. What you need to do to make an impact can often be less work than you imagine, like work that removes unnecessary layers.
If you can name a few project ideas where you feel it'd be impossible to make an impact, we can try to provide examples of how to attack them.