It's not at all true that anything other than a line sensor is a waste, just that you're throwing away useful data if you downsample a slow array detector to use it as a line sensor. A 240 fps camera would be awesome at just about anything local/states/regional if you can identify numbers and step through the individual frames without having to do any processing (i.e. just capture to the computer and start stepping). When a few cameras started coming out with those kinds of speeds ~4 years ago it looked like they didn't use frame based file formats, which makes them hard to use as a finish camera. Even a 30-60 fps camera works for most purposes if you can get a 1/1000s shutter speed. I have a $150 MiniDV camera that works great for local races.
But here's a page full of linescan cameras (need lenses still) that would mostly work and be less than a finishlynx. Least expensive is about $1500 and has 2048 px (plenty to put across a road) and ~50 klines/sec:
https://www.machinevisionstore.com/C...gory=1&group=2
Not quite cheap enough for hobbyist territory, but close if you're going to start a finish line business.