Question: My understanding is that Masters and PhD students often need to TA -- even if they're already research assistants to a professor. 

I'm a first year undergraduate who took courses heavily TA-reliant last semester. My impression is that my TAs (oh they were helpful people) don't really get much out of TAing. The job just covers some of their costs and their tuition.

Sure, you may learn a bit about teaching others, but I doubt that you may learn much after three weeks of doing so. Many of the users on this site were once or are TAs. Do you agree with my view?

If TAing is really a necessary evil, are there better ways to fund your education?

Answer: 
I understand that it might often be thought that one learns little more after TA'ing for a few weeks, or a year, or a few years.

However, I strongly disagree. I have seen no cases where anyone came to a profound understanding of the psychology of 18/20-year-olds even after years of dealing with them. Nor understanding the complicated, self-contradictory goals of lower-division mathematics. Nor... Many research-oriented people in math never do quite catch on, although the norm is an uneasy truce with the seemingly-ineffable realities.

I truly think that until one can nearly-effortlessly do a bit (of course, hours within some limits...) of TA'ing, one has not understood the situation of academic mathematicians, and does not understand the job itself. (The "research" aspect has its own invidious pitfalls, but/and these are fairly different, perhaps opposite, from those of TA'ing.)
I think TAing helps in evolving a graduate student's character. Teaches him/her how to plan courses, interact with students and enhance public speaking/presentation skills. Its the another road "step" into academia (other than research). Perhaps that why it is necessary in many schools even for those appointed with full research funding. 

What I don't like about the current system is that TAs tend to teach the same course over and over again! It gets boring and many loses motivation. Also, there can be many grey and shady areas between professors and TAs/graders. For instance, professors asking TAs to do the bulk of the work, being available for extra office hours, write exams, update notes etc. In such cases, TAs tend to agree to these things "most can't even say No!".