I have a Giant Cypress (cheap $300 hybrid). My rear wheel started breaking spokes at about 1000 miles, and I was breaking a spoke almost weekly for several months. Finally I said screw it, bought a new rim and butted DT spokes and built a new wheel. This one has 10,000 miles on it with zero troubles. So I'd say yeah, build a new wheel.

I had never built a wheel before, but with Sheldon Brown's instructions and some patience I had no real problem.

I built a truing stand from 2x4s, a couple of shelf brackets and some aluminum that I cut notches into to match the axle. I put a bit of threaded rod through a junction nut attached to one of the uprights as an indicator. Cost nothing, just junk I had lying around.

I dished it by adjusting things until the rim was just touching the indicator whether I flipped the wheel around or not.

I just built a new front wheel too so I could put disc brakes up there. I never bothered with a tensiometer; a friend said "just start tensioning everything up while keeping it true, and just put as much tension on it as you reasonably can without going nuts; just stop before you start to strip things". I also just plucked the spokes and got the pitch of all the spokes on one side of the wheel pretty close (within about 1/4 step I'd say). ISTM that's probably a more accurate gauge of tension than a tensiometer, at least as far as getting them all the same.

I've even seen resources online for determining the tension of a spoke given its pitch, so you could just use a pitch pipe, keyboard, or tuning device as a tensiometer.

I'm sure I could have done a little better with $200 of equipment, but given that it was a first wheel build, I did it with $0 in equipment, and it's still dead true after 10,000 miles, I'd say maybe the $200 isn't necessary for the occasional builder.