Maybe we just need overhead projectors back.

There were a few things wrong with them (painful to look at while operating, and the bulbs tended to burn out if you moved them around while turned on) but fundamentally I don't think they were broken technology. Overhead projectors would be well complimented by computer projectors, but computer projectors make a poor replacement for them. Attempts to replicate the advantages of overhead projectors on computer projectors always fall flat, as far as I have seen.

I think the demise of overhead projectors is an example of a regression caused by our tendency to have rose-tinted glasses whenever considering more technological alternatives to existing technology.

In university we have cameras over some parts of the professors table which are directly projected on the screen. Works great without the the drawbacks of an overhead projector.

I think that is probably the solution. I've seen somewhat similar systems that tried to be more technically advanced than that, but they always made things worse. Just a straight-up camera-feed to the projector would work great though.

The advantage of these over overhead projectors would still be pretty small though (really only the being blinded and replacement bulbs issue), so you would need to ensure that the system is rock-solid reliable. If not, then you've just made it worse by making it more advanced.

Document cameras like this work very nicely, but there is one small downside I've noticed: their framerate tends not to be very good. That's usually not a problem at all, but I have a couple of physics demos where I roll things around on an overhead projector, and the document camera often can't keep up with quick motion. Simple analog light and shadows obviously have no issues with that at all.

overhead projectors are a bit dimmer and can't make nearly as big (or uniform) an image as the document cameras can.

Exactly this, in university one of my professors in first term rather than using slides, printed his slides onto paper and put them under one of these cameras, visualisers as they're called. I found it much more engaging since he could easily annotate things and just get a blank sheet of paper if anything needed further explanation.

When I attended lectures with such cameras (which was some years ago) they were pretty horribad. Low contrast, low framerate, and motion blur everywhere. Probably had tons of latency too.

My math professor hooks her Windows tablet to the projector and then draws on that using Onenote which works out pretty well

Interestingly decent second hand overhead projectors are going very cheaply on eBay.

MS Surface attached to a projector. Done.

Seems like an ipad is pretty close to what you want. If you could project part of the screen and leave some left for nav, new slides etc. then you could draw at will and be able to jump around slides without having to disturb the audience while you fumble around for it.

iPads are OK but not ideal for this sort of thing. Because they're capacitive (rather than resistive) touch, writing is relatively coarse and crude and you have to be somewhat careful with false pickups from your palm. They're usable to draw on but it's not like writing on an overhead foil or a piece of paper.