I think VFDs are great. I currently am only running one, on my vertical knee mill, 1ph. I have one on a 1941 Rivett 1020 with a 2ph motor (which I've sold to a good friend). I installed them on two Bridgeport vertical knee mills for a patternmaker friend, one 2hp, the other 3hp. All were TECO FM50. All were set up for variable speed and reversing operation. I've never felt there was any significant loss of power. The ability to run my mill down to almost no revolutions and instant reversing is an extremely valuable feature. Allows me to do rigid tapping.
Installing the FM50s has been easy, once I'd done it once, but there was a bit of learning curve. An installation without speed control or reversing would be a snap. One "trick" is that VFDs do not like external switching, so the On/Off switch of the bandsaw would have to be rewired to route it through the VFD. Terminals are clearly marked, though, so it isn't difficult.
One thing to consider is that VFDs usually like 220v input rather than 110V, although there have been 110V units available.
The FM50 series is now discontinued. The replacements are the FMX TD200
series. I've not done one of these, but believe they would be similar.
If your 1950 3hp motor is in good working condition, I see no reason why it would not work just fine.
I would be interested to hear more from David about why he thinks a VFD would not be a good application. While not taking advantage of the variable speed or reversing capabilities, it would allow operation of the bandsaw with full power without having to replace the motor.