MX Tires on Street?

Why not? (Other than Jonny Law)

Compounds overheat?

The reasons are:

1) They wear out quickly because...

2) There is no DOT approval on the side wall (which is where the law comes in) because...

3) There is not a lot of rubber touching the road at any given time compared to a bona-fide street tire, even a dual-purpose tire like the WR-250R comes stock with.

The knobs of an MX tire are shaped and positioned so the angles of the knobs have their sharp (when new) corners and edges biting at the ground for grip, but when that ground is pavement that's harder than the rubber tire is, you get just the opposite (no grip when you might need it).

You can see this easily by comparing an MX tire such as a Bridgestone M404 or Dunlop MX51 with even an aggressive DOT-approved dual-purpose tire like the Dunlop D606.
The knobs of the D606 are curved in order to conform to the road surface when leaning the bike from side to side while cornering.
The MX tires, by comparison, intentionally have the corners of their knobs sticking up like spikes.

This is one of the reasons an MX tire will wear so fast on the street - the sharp, pointy corners of the knobs don't offer a lot of total area of rubber carrying the load and torque, so it's like using an eraser on the end of a No. 2 pencil to provide all of the traction to move a strip mining dump truck up a steep hill (if you don't mind an exaggeration).

4) The rubber compound is made for specific kinds of off-road terrain, and pavement isn't at the top of the list.
I also wouldn't be surprised if the tires carried a low speed rating.

5) At typical off-road tire pressure (10 - 12 psi), the tire will flex a lot and get hot at speed on pavement, adding to wear.
Try to combat this flexing and add air pressure, and you have less rubber touching the road.

On the flip side, MX tires off-road = the best traction you can find, especially when using a tire made specifically for the terrain.

The only difference between an mx tire and a dot tire are the dot tire was sent in for the dot test!
Tire manufactures dont bother sending tires for the dot test if they dont think people will be using them on the road as it cost money.
Look at ac10s, pirelli scorpion pros, kenda trackmasters and parker dt, a bunch of mitas, maxxis en, plus a bunch I've forgetten, they're all dot mx tires.
Some non dot tires (maxxis maxcross it) last and work better on the road than alot of dot tires

Yes, the Michelin AC10 I have here leaning against the wall (which I don't like as much as the venerable Bridgestone M22) has DOT on the sidewall, even though it looks like a full-on MX tire.

The M22 grips the road well enough to get by but wears pretty fast, and it will be a matter of only a few days of street use before it's worn enough to be considered spent when you get back off the road.