I think this is the 3rd thread on a related topic in the past couple days, and it's gotten me thinking two things:
One: it sounds like parents are taking a lot of responsibility for both the parties and the gifts. Which I totally understand for very small kids (2-3) but starting at 4-5 my sisters and I were heavily involved in both planning and attending parties. Planning in the sense of: who do you want to invite, what food would you like, and where would you like to have it (home or park, which park, etc...entertainment venues were off the table for us but that obviously varies for families; maybe your home is small so you're ok with certain venues but not others). Gift-giving in the sense of: what do you want to give your friend/what does your friend want? At younger ages I'm sure the choices were somewhat guided, at older ages it was "your budget is $20, unless you can find someone to do a joint gift with". I mention this because, thinking back, both were pretty good learning experiences. One about making decisions and planning, the other about empathy and thinking of someone else's wants rather than one's own.
Two: I assume your desire not to give gifts comes not from cheapness but from a desire to curb materialism and waste (as you say, there's a social contract that if you take advantage of someone's planning a party, you give a gift). Or you're tired of thinking about it, in which case see #1 and make your kid do it. But, if it's just not wanting to give junk, it's worth thinking about what "things" (not necessarily material) you value about childhood and gearing gifts (not necessarily material) toward those ideas. Some things that were popular in our social group growing up:
1) Art supplies. My friend discovered cross-stitch and calligraphy and I discovered polymer clay (Sculpey) this way. We also did some sewing and knitting from kits we got. It's still stuff, but it teaches DIY skills! I remember we were big fans of Klutz books for their cute included supplies and their fun-to-follow directions. YMMV though.
2) Board games. Many of them we still have (and play). Some of these get expensive though, which brings me to...
3) Joint gifts. $15-20 was pretty standard gift value in our circle(s) but sometimes 2-3 families that knew each other well would band together and get one nice thing instead of 3 junky ones. I think it worked well.
4) Sports equipment. I'll be honest most of this was pricier and thus came from parents (rollerblades, etc). But we were obsessed with Chinese jumprope for a while (that's the one where you put an elastic around your legs). In the Age of Screens, anything to get kids excited about the Real World, neh?
5) Books. We were all avid library patrons, but these were still always appreciated.
Of course, we got our share of Barbies, etc. But it probably says something that I remember lots of the above and not a lot of the more standard toys.
Final note, sometimes it's not exactly about what the gift is, but how it's presented. A young, close family friend was turning 5 or 6 when I was 13 or 14 and nobody in my family was inspired with what to give (all the above ideas seemed exhausted). We ended up in a Hallmark store of all places, and they had these plastic dinosaur eggs with stuffed dinosaurs inside. They were cute and we were desperate so we got her one; then I sat down and typed up some detailed, formal instructions about incubating and caring for your baby dinosaur. Apparently she was obsessed about it for quite a while; the parents had to sneak into her room at night to "hatch" the dino after a few days! (They seemed amused, not upset, by this.) It was still a stuffed animal, which we all had too many of by the end, but at ~$10 it was less than our usual birthday gifts for friends this close; the extra effort made it a pretty unique gift, though. I could see this working *really* well around gifts of experiences... give a kid a "treasure map" and then take them on a hike to find the "treasure"/gift (chocolate coins + costume jewelry or craft rhinestones?). Give them a flashlight and a smores kit and invite them for a real or backyard campout. Give them a "field guide" (i.e. notebook or coloring book) and invite them to the zoo (if you have a cheap or free zoo around).