I actually know a lot of serious collectors, who spend varying amounts of money.
In general, people don't dive in at the $20,000 level. They start out with much smaller, affordable items and gradually work their way up as they learn more...and sometimes their collections appreciate along with them (I can think of two separate people with extremely valuable collections now who specifically took an interest in that area because it was affordable.) It's also pretty common for collections to self-fund in a way--collectors sell some items to fund others. So the cash outlay going into it may not be as big as it looks.
As to why--a lot of them love history and find the experience of basically curating their own museums and living with historic objects to be really fun. There's also a big social component, as with any community with a very specific interest, and the "joy of the hunt" is a part of the human condition, I think. As has been pointed out, there are also lots of opportunities right now to acquire very high-quality items for (relatively speaking) not a lot of money. As the Baby Boomer generation and their older siblings start to downsize, people are finding that in many cases children and grandchildren don't want the items they have accumulated or received from their parents, and so the market is flooding with nice 19th and 20th century items. (Earlier, not so much, as they are rarer--but even those prices are dropping.)
The other thing to remember is that TV appraisals are often very generous. It's not that the appraiser is lying, but they certainly give the most generous upper estimate they can get away with...and in many cases, that's based on market conditions of a few years back that are not applicable now.
