In theory you CAN operate a motor that was originally designed for 50 or 60Hz at 590Hz. But theory and reality have a way of diverging. For the moment though let's ignore most of the details and cover the big one.
AC Induction Motor design is dependent upon a relationship between applied voltage and frequency, what's referred to as the "V/Hz ratio", to produce a given amount of torque at a given speed. So a motor designed for 460V at 60Hz has a V/Hz ratio of 460/60 = 7.67 (to one), motors designed for 380V 50Hz have a V/Hz ratio of 7.6 (the similarity is not a coincidence by the way). Maintaining this V/Hz ratio (+-10%) allows the motor to produce rated torque at any speed, up to the design speed. If you only reduced the voltage without maintaining the ratio, the torque drops at the square of the voltage change, so the motor stalls very easily. What a VFD does is to allow you to attain that rated torque from the motor at any speed below the designed speed without stalling.
If you operate the motor at a frequency above that which it was designed for, the first issue is that you can no longer maintain the same V/Hz ratio; you "run out of voltage" because the VFD output voltage is limited to the VFD input voltage (or less). For example if a motor is designed for 460V 60Hz, the drive will provide 460V at 60Hz, but if you increase the frequency, you can no longer increase the voltage with it. So above the base frequency of the motor design, the effect is the same as decreasing the voltage; you begin to LOSE torque. At some point your motor will produce so little torque that it can no longer even accelerate the mass of its own rotor and it stalls. Such would likely be the case for a 50 or 60Hz motor that is given 590hz.
Long before you get there however, those other previously ignored reality issues will bite you; the bearings are not rated for that speed, the mechanical balancing of the rotor (not to mention the load) will likely become so bad that it flies to pieces, and the cooling system for the motor will cease to function, burning up the windings.
VFDs OFFER those higher frequencies because it is POSSIBLE to buy motors that are custom designed to operate at higher frequencies. These are often referred to as "spindle motors" because they are used in high speed machining applications.
Side note: the limit to 590Hz is the result of a world-wide restriction implemented to avoid having the VFDs be used in uranium enrichment centrifuges, which need to operate at frequencies somewhere above 600Hz (we don't know exactly where). Not all countries adhere to this restriction, so there are VFDs that can go to 1,000Hz and more. They just can't be legally sold in countries that DO adhere to that restriction, mainly North America and EU countries.