What is the largest obstacle in practical helium-3 fusion?
I just found this now, sorry for the tardy reply.
Very simply, He-3 requires much higher temperatures to occur, occurs less often than D-T even at those temperatures, and produces less energy when they do occur.
Since a working reactor should produce more energy than it consumes, the fusion reactions have to be plentiful enough to produce more energy than is being naturally lost to the surroundings through convection and radiation - the same as any hot object. When the self-heating from the fusion events provides enough energy to keep the fuel hot on its own, we call it "ignition" or a "burning plasma".
The rate of losses goes up with temperature, so He-3's higher operational temperature means higher losses. Combine that with lower rates of production and lower output from those events, and you have an extremely difficult problem. In overall terms, D-He-3 fusion is perhaps 1000 times more difficult than D-T.
We've been working on D-T for many decades now and we're still about another decade away from that hitting ignition. So He-3... well, that's just not going to happen.
Now you will easily find any number of people claiming they have some sort of shortcut to He-3 fusion. You can discount any such claim.