Mountain bike tyre at road bike pressure

No. It makes no sense to run a large tire at high pressures. As indicated in the comments, modern cycling has now accepted that higher tire pressure does not equate to lower rolling resistance in the real world.

Further, the ideal MTB tire (presuming there is such a thing, which there is not) requires tread to bite into soft surfaces. What tread pattern and depth changes depending on the surface - rock, mud, sand, hard pack to name a very few. Surfaces change from moment to moment, so choosing a mountain bike tire is far more complicated and important than a road bike. Most MTB competitive bikers change tires for the conditions of the day, and many recreational riders swap between tires regularly, this despite the manufacturers spending decades looking to the ideal all purpose tire.

A better approach to the ideal bike is lower the cost of bikes to allow for a bigger N and S. (Refer https://www.velominati.com/ rule 12)

Even though pumping up your MTB tires harder will help with reducing rolling resistance on the road, 100-120psi is far beyond what you need. 50 to 60psi is already getting too high, and most tires can handle that. However, not all rims can handle that kind of pressure, so you’ll want to be aware of that. Perhaps select wide road bike rims if you really need to go that high.

Ultimately, the thick tread, thick/stiff casing, and soft rubber used on MTB tires are guaranteed to roll slowly. At some point, you might be faster carrying a set of road tires to swap on when you need to ride on the road.

2.00 or 2.20 or 2.30 inch tyre that I would use at 7-8 bars (100-120 PSI)

Does such a tire exist?

No.

A little math...

The surface area of a torus is 4 x pi^2 x R x r, where R is the large radius of the wheel and r is the radius of the tire here.

Let's put a 2.00 tire on a 29er rim...

4 x pi^2
  x 15" (approx radius of wheel at center of tire cross section)
  x  1" (radius of tire's surface)

= 592 in^2

Assume the tire surface area is only about 2/3 of that, or about 400 square inches. (It's probably more...)

Pump that tire up to 100 psi and each of those 400 square inches of tire surface has 100 pounds of pressure pushing on it.

That's a total of 40,000 pounds of force trying to push that tire off the rim.

Even if the tire can hold, the bead of the tire will be pushing HARD against the rim, trying to tear it apart.

40,000 pounds of force for a 2.00 tire at 100 psi. Pump a 2.40 up to 120 PSI and it's more like 50,000 pounds of force.

There's a reason why tires have maximum pressure ratings, and larger tires have lower maximum rated pressures, and it's not because higher pressure starts to increase rolling resistance.

It's because high pressures in a large tire are downright dangerous.

The other two answers noted that large tires can't be pumped up to high pressures.

Let me explain a practical solution to your problem:

• Buy a gravel bike or hybrid bike with ample tire clearance (depending on if you want drop bar or flat bar)
• Build two sets of 622x19C rim wheels
• Put knobby wide tires on one wheel set (with these rims you can go up to 44mm)
• Put narrow high pressure road tires on the other wheel set (with these rims you can go down to 28mm)

If you want puncture resistance, there's a solution: tire armor made of foam. My recommendation would be not to use this on the road bike wheel set, but on the MTB wheel set you may want to use it.

The only problem with this plan is that you have to decide which wheel set to install before going to ride. Thus, most gravel bikes have tires of intermediate width that are a compromise between road and MTB uses, simply because one has to ride quite a lot on a road before arriving at the MTB trail.

You can't inflate wide MTB tires to road tire pressures. And it's not just that there are no tires that support that, it's just as much that there are no rims that support it.

The air pressure within your tire puts the tire under tension. How much tension is determined by both the pressure and the curvature of the tire. The slimmer the tire, the higher the curvature, and the lower the tension for the same pressure. As such, a 2 inch tire at 50 psi has pretty much the same tension as a 1 inch tire at 100 psi. All the pressure ratings for tires of different widths typically produce just about the same tension of the tire material.

Now, the tire tension translates directly into the force that the tire applies to the sides of the rim. Again, all tires within their respective rated pressures put just about the same amount of force on your rims, independent of whether they are road tires, or balloon tires. If you create a tire that allows twice the pressure as normal tires of the same width, that tire will put much more force on the rims than they are designed to hold. Most likely, you'd get a failing rim before you get a failing tire!

As such, no tire company wants to manufacture such tires, it would require them to also supply heavy duty rims, and explain to their customers that they must not use their tire with any rim that is not specially rated for the use of such a tire.