If you hire aides on your own, then you and not the agency decide what they can do. Also, you have more flexibility in terms of credentials. Depending on your state, CNAs, NARs, NACs, HHAs and [pre- or in the professional program] OT/PT/nursing students, just to name a few, are all possibilities. The coursework + clinicals for CNAs, for example, is only of several weeks' duration and is not deep -- I scored 100% on the practice written exam off the top of my head, and the clinical exam is, shall we say subjective, based on several accounts I've heard. So there's no magic in the prep -- it's in the person. You could even find someone you know/like/have referred to you and pay for their coursework, if/as appropriate. Or just train them up yourself. If s/he wants to learn and do the right thing, shows up and works hard, you are there.
YMMV, obviously, but in interviewing/trying out a broad range of assistants recruited via various means, we have found that young students are a better fit for us, and you are not going to find them at agencies. We have tried out some people that were previously/currently working through agencies as well, and they just weren't for us.
I'm not saying that everyone who works with an agency is so mediocre that s/he needs an agency to get work, but there are plenty of good people who, all else being equal, prefer not to give a good chunk of their earnings to the middleman. And you pay extra for that that agency cut as well.
For those that have an agency they like and can afford, of course, whatever works. The foregoing is directed toward those for whom that is not the case.