I usually highly recommend the VFD options but you asked for reasons for NOT going with the VFD.
A VFD can cause some AC line notching and high frequency harmonics reflected onto your power system. IF this is a problem you can add line reactors (inductor) or harmonlic filters that are designed for VFD applications.
A VFD can potentially cause premature motor failure in very old motors. Real old motors built before VFD's were invented, when operated on a VFD may run hotter than on a pure sine wave voltage. This is due in part to the motor laminations and causes of the PWM voltage. Note though that a static or rotary phase converter will not have a pure sine wave like 3 phase from the power company either, and the VFD might be the best choice aside from the grid power. To further soften the pwm voltage to the old motor you can install a "load reactor" (basically a 3 phase inductor) between the motor and VFD. I usually recommend a load reactor on older motors.
Applications on motors with extremely long wiring between the motor and VFD, like 500-1000' may have issues with "reflected wave". This should not be an issue in a home shop but is experienced in industrial installations and causes new motors to fail. There are other problems with long leads but the topic is most likely too in depth and irrelevant to this forum.
A VFD uses PWM in the audio spectrum. Some motors depending on mechanical construction can "sing" or act like a speaker at that frequency and the noise, although not louder than the power tool, can be annoying. This occurs mostly on older motors where the windings are not secured as well in the motor. To minimize this a load reactor will reduce the volume, and or you can increase the PWM frequency to reduce it as well.
A VFD can cause bearing currents that can eventually destroy the motor bearings. The PWM frequency can induce a high frequency component into the rotor and this voltage needs a conduction path to ground. The current is low and akin to a small static electricity charge. The problem is that this discharge occurs at the bearing race and can damage the race. In 24/7 motor operation, the motor bearings can fail before they would otherwise. In a shop application, this is almost not a concern. In industrial applications where this is a concern, a carbon brush is placed on the motor shaft and connected to ground.
I still highly recommend the VFD option though but usually I add a load reactor to resolve the possible PWM noise issues and it also fixes other possible problems as well.
The VFD may not be sized accordingly, most manufacturers rate them nowadays with global marketing, marginally. What I mean is that they might be able to supply 150% rated current for 3 seconds and 110% current for 60 seconds. A few years back the US made VFD's were rated at 150% for 60 seconds. The US has changed to Asian ratings to have comparable pricing. More current is more HP, so if your table saw hits a knot in the wood, your 3hp motor is a 4.5hp motor for that amount of time. The motor can do this without damage as 150% for 1 minute is usually within the motors overload curve. A RPC will be able to supply this power but a VFD may not if it's not sized properly. IF you need this capability sometimes you may need to buy a 1.5hp VFD for a 1hp motor.
I didn't include any disadvantages of the RPC or SPC because the list would be much longer.
I've used VFD's for variable speed on my wood lathe.
I've installed VFD's on a 3HP and 2HP knee mills with excellent results.
A VFD can also give you increased starting torque while keeping the motor current below rated current compared to starting across the line which yields less torque and 6-10 times rated current.
Brian