No. You should not be spending $200 on teams of teachers. I make cranberry nut bread in the small mini-loaf tins that I get for 30 cents at the discount store, and wrap them in cellophane with a piece of curly ribbon. I give these to the FedEx and UPS drivers who always give my dog biscuits with every package delivery, the garbage collector, the plow guy, the newspaper delivery guy, the letter carrier, and the pharmacists. You could do that with teachers, including physical ed/music/art for far less than the $5 or $10 gift card, which would in turn require the teacher to lay out money of his/her own 90% of the time to "top off" the card. We have a local bakery that makes fabulous oversized brownies for $2.50 each - sometimes I give those in a cellophane bag with some ribbon, and the bakery will also cut 4 different flavor brownies into quarters, put them in little paper cups, and then wrap 1 mini-bite of each of the 4 flavors in a bag or little box. So everyone gets a bit of fudge walnut, a bite of raspberry chocolate, a bite of blondie, etc. They look adorable and cost $2.50 each AND support a local business.
Unless you have a room parent who will collect money from every parent and organize a group gift (which we do in elementary school but it breaks down in middle school when kids are so split up among so many teachers), go small. Include a nice handwritten note - from the child - about the teacher and offering good wishes for the new year. Done.