We are on the unschooling spectrum. We are not radical in all areas though we are in many. (We limit screen time and sugar consumption. We believe kids have a responsibility to help around the house.) How people feel about those types of issues will probably influence their answers.
I have bought my kids TONS of toys. Most of them I have selected since our kids are still young. Most have been purchased at thrift stores or from craigslist. Almost all our toys are geared towards creative play. I read somewhere that kids benefit from having a wide variety of toys to explore the world with. Every one of our toys has a spot on a shelf or in a drawer or bin. I've known kids that had so many toys that just laid on the floor (literally knee deep in a huge room.) Those kids did not know how to play with toys because it was all so overwhelming. Because our toys are neat, the kids can easily see them (except costumes that are in a dresser) and access them. They naturally rotate through their toys. For awhile one toy is popular then later it's another.
My son LOVES to play at his "bakery" (a wooden kitchen) with playdough. We have costumes I bought for $1 or so after Halloween. Rubber boots that can serve as firefighter boots (or whatever the kids think of.) Grown up shoes and clothes from the thrift store. Wooden trains, a tent with a tunnel, shape sorters, puzzles, a stroller, dolls, a weebles treehouse, legos, puppets, musical equipment, cozy coupe cars, shovels, buckets, etc., etc. Cooperative play games (Harvest Time and Snowstorm are the most played.) Did you notice nothing is a character? Very few have batteries. We have a lot of art supplies and several hundred books that have all been read multiple times.
We don't allow our kids to watch TV, though our son can get on youtube or watch documentaries (or play a very select group of computer games) while his sister naps. He knows who Thomas the Train is even though he's never seen the TV show (we have 2 Thomas books we were given.) He also knows the Winnie the Pooh characters from a couple books. He thinks the Toy Story cowboy is Cowboy Kirby from the great book "Splitting the Herd." He is not obsessed with the characters he knows. We just bought both kids matching train pajamas. They're Thomas but Thomas was not the draw, it was the fact that they were trains.
When we go to the store, my son naturally wants much of what he sees. The other day I bought him the rain boots that look like firefighter boots even though he has two pair of rubber boots at home. However, these were real firefighter boots and my son is really into firefighters. How could I say no to that request? But the majority of the requests I just nod my head to. He rarely asks for the things he sees once we are away from the store.
Actually, for his birthday last year he only wanted one thing--a battery operated toy guitar with a plug in headphone microphone. He saw it in a toy catalog. We got it for him even though he already had a battery guitar without a headphone because it was the only thing he asked for. He has played with it quite a bit.
For his birthday, he got $20 from his grandmother. I told him he could put it in his piggybank until he decided what he wanted to buy. He told me he wanted to use the money to buy his sister a piggybank just like his. A couple months passed before he said, "Can I use my money to buy this?" We were at the store and he wanted an overpriced sidewalk spray painter. I told him if he asked me again in 2 days I would bring him back to get it. About a month later he spontaneously asked me to take him to the store. He spent the whole $20 on the painter and extra paint. (Enough for about 4 play sessions.) I would not have chosen that gift for him because of the expense, but it's what he wanted and it was his birthday money so I agreed. He thoroughly enjoyed using it. I doubt if we'll buy much replacement paint.
We budget a certain amount of money each month for toys. (It's not a lot of money.) Although I tell my son we must choose how we spend our money wisely, I haven't shared budget numbers with him yet. I'll do that someday. I think young children should just be given toys as part of their life-tools. As they get older, they need to start earning the money to buy stuff. I think it is reasonable to help a child find a way to finance their desired purchases by offering to hire them for assorted jobs. Our kids have to help around the house because families work together, but if they want to buy something special (that I don't feel I should be providing) then certainly they can get a job to earn the money they need. (We haven't started allowance yet.)
As far as working together on a budget, I think that's reasonable in a limited fashion. We decide the overall amount of the kid related budget and they can help develop how much goes towards activities and how much goes to toys and books. (I'm not sure about the whole voting thing, I'd rather it be a discussion.)
I think commercial TV is pretty evil. The whole toy buying thing is just one reason. (Our son doesn't really understand the concept of TV. He just knows kid documentaries. We don't even watch kid movies.) We don't have to put up with the toy-crazies that TV/movie watching kids can have. It's pretty nice. (I did buy my kids and their cousins zhu zhu-type pets for Christmas. My kids play with them because they're fun. My TV watching nephew was thrilled to get it because he'd seen it on TV, but I don't know that he actually liked it. They don't live up to expectations if you've seen them on TV.)
BTW, I do buy a lot of duplicate toys. We had two sets of roller skates before our daughter came along and two cozy coupe style cars. When friends came over there was a set of skates or a car or a pair of rubber boots or whatever for each kid. A lot of parents have stated they thought this was a brilliant idea. Since I buy these used, they usually don't cost much, but it has made playtime a lot easier around here.