Inductor as current source
The inductors limit the maximum output current of the inverter. Replacing the inductors as you suggest will reduce the maximum current to 1/10 of the original maximum current (at resonance).

It is common in the induction heating industry to refer to an H bridge with inductors in series with the output of inverter as a "current source". The word "constant" is Not used. The inductors provide current after the active devices are turned off. The series inductors do not substantially affect the resonant frequency of the tank.