he system is ineffective.
I don't know about that either.
I'm assuming that it is a rotary frequency converter set with a single phase 30hp drive motor in which case the 40kVA transformer rating might be the minimum required to start the drive motor and may run significantly below that under steady state conditions. I don't have much experience of single phase motors and none at all at that rating so thus can't judge what the starting current might be nor what available methods there are for mitigating starting currents.
And, if it is a rotary converter, then I do agree with your point that a solid state inverter would be more efficient, considerably so, even if you had to use a transformer to get the right voltage. A variable frequency drive might fit the bill quite well depending what kit is hanging on the end of the three phase supply. If there are any controls associated with the motors the customer wants to run the controls might not take kindly to a variable voltage variable frequency supply.
But there would still be the supply capacity limitation. The15kVA simply isn't anything like enough. Even with solid state conversion.
I'm not sure about the capacity of a 30hp converter either. I think that could be a bit marginal considering that the customer has a 25hp motor according to the OP.