That's not a "false" Vmo restriction. It's real, and not there because we don't trust pilots to stick to some ICAO 'speed limit'; it's there because the aircraft could not be certified with a higher speed at those altitudes.
Birdstrike is a real cert requirement, we don't get the option of saying to the authorities "go on mate, let's not worry about birds, it's never gonna happen". Even if the "speed limit" you mention were totally waived, the Vmo would be unchanged. It's a design restriction, not operationally motivated at all.
Also, there are similar Vmo cutbacks on the CRJs (I don't have a chart to hand) which are also, IIRC, birdstrike-driven. (I think it's a cutback from about 335 to 300, but that's pure memory and could easily be wrong)
Finally, be aware that while the windshield may be the most critical birdstrike case, by increasing speed to 300kts, you're increasing the birdstrike energy by some 50% above the assumed certification level. At some point you're going to get to the point where OTHER strikes are going to cause damage - especially if you hit a bird above the certification mass.