It depends on the use of the mountain bike. Do you use it as a mountain bike? Or do you just use it on paved roads and cycling paths?

The MTB world is shifting towards wider and wider tyres to be faster. Even in cross-country where the world cup riders now regularly use 2.3" wide tyres. Such wide tyres are faster in a real MTB terrain, even if just cross-country and not enduro or downhill.

For cyclocross racing, the tyre size is kept at 33 mm by the rules, but most often the riders would happily go for wider ones, if they were allowed to do so. It would make them faster on the cyclocross course.

After the question edit:

If you just wast to be fast "of course" on a flat road than you mainly chose the wrong type of bike. It will never be as fast as a road bike but it can be made faster by dedicated for road use. These will be more narrow and have little tread (perhaps even slicks). The width will depend what your rims allow but remember that even in road racing the tyres get wider, 28 mm is now the norm. Do not become obsessed with as narrow as possible. The design of the tyre specifically for roads is more important.