Race-winning quads that cost <$150? Yes.

This build exists as an example of what a very lightweight 3" racing setup can do, especially given the budget required to build and operate this type of quad. I can show up at races and put down podium times with these, often as fast our faster than my 5" setups. Just about the only downside is that these little punks lose every time when I have midairs, but it's shocking I can keep up well enough for that to be a problem.

These are eminent budget racers - got the frames on sale for $15, the motors were $10ea, Spedix IS20 is a great budget ESC, and the F4_SVTX is a great value FC/VTX at $23 (just runs really hot in the summer - set up and use the pit mode!). The batteries are CNHL and Turnigy 4S 650mAh and 850mAh packs, although I've ran these with 1000mAh 4S packs at times. Needless to say, these rip no matter what, although the heavier packs don't add much flight time, just more available amperage in punch-outs and straight line sprints.

The build itself is shockingly simple if you have 6-pin JST looms just hanging around, that becomes a quick and simple re-pin. The XM+ wires up easily, although my attempts to get an XSR with full telementry haven't worked. Tramp VTX control onboard the VTX does work well. Needs a bit of a stress loop on the U.FL antenna to be comfortable, but in this frame my added 25V 470uF capacitor actually provides a good stress relief point for the antenna to be taped to. This setup handles crashes shockingly well, especially at the speeds I end up going.

Biggest downside with the frame is that it requires a Nano camera - helpfully the RunCam Nano 2 is pretty affordable, but lacks some features I'd want to be able to adjust (PAL/NTSC switchability, image profiles). Even that goes away pretty promptly as a downside, because these are just such a hoot to fly.
I'll probably upgrade these with the Predator Nano V4 when they become available, because I like the FOV on offer from 1.8mm lenses, but I struggle with altitude management on some of the more fish-eye image camera setups.

The FC/VTX in 20x20mm form factor is a limitation when it's hot - if you leave it on, no matter what power, you'll have about five minutes before the VTX starts to do its thermal shutdown routine - do take advantage of the Betaflight low power capability if you plan on running more than 25mW output. Even then, on hot days, 25mW is enough to get the FC temperature up above 85°C in just a couple of minutes, so you'll want to put it into pit mode (even if you have to navigate OSD menus to do so). That's the one serious drawback of this setup, otherwise I do really enjoy having that integrated. A Rev2 of this setup that accepts ESC Telemetry and current sensing would have me willing to pay twice as much, because it enables some really lightweight and low stack height builds.

Propeller selection is an interesting one, the Gemfan 3052's are really fast and keep me on pace with 5" quads... but don't help much with efficiency - I tend to run these on 850mAh packs to do 2 minute races. With the lighter Asteroid frame I can get pretty close to race distance on a 650mAh pack, but I have to either back off in a few spots where I don't make up much time, or risk running out of battery after the 1m:30s mark.
The Gemfan 3028 Winddancers are super efficient props, with excellent control feel. The downside is the speed is fairly low, and with heavier packs the thrust on offer isn't that huge.
Efficiency isn't the greatest when pressed hard - but flying at 9/10ths these will achieve 3 minute flights readily at speeds which most people would expect to need a 5" 6S rig.

These basically are my track recce rigs, and exploration setups, but the durability in this build allows that. I do think that the weight offset of running a more conventional flight control stack and an AKK FX3 (or iFlight Succex stack) would help out, as would running a pigtail. There have been whole days where I just run these because it's lots more fun.

For anybody on a budget, it's really worth giving a 3" racer a try.

Being able to run <$8 batteries, having ~$165 complete builds with high end parts, and the ability for these to absolutely shrug off most small crashes make it a phenomenal setup for racing and having fun.

// Edited to add: //
This was actually my fastest race quad at the Albuquerque Balloon Museum Pod Racing BMPR-12 race, putting me on the podium. Shockingly fast 3" setup, I'm building more of them and letting other more expensive quads languish because this is so good.

// Next Edit: //
This is the winning quad from the Texas Drone Champs qualifier of the El Paso & Las Cruces chapter... totally floored by amazing performance on offer from these little guys - I guess I'm building more of them.