Hmm. A MOSFET for a motor switch might be overkill. Also, there's no flyback diode. So your Pi pretty much will let its blue smoke out when you get a flyback voltage, or at least the MOSFET.
So your suggestion is actually introducing a second magnetic field, so now you've doubled the chances of blowing up your Pi and or the MOSFET.
Whether you're using a transistor/MOSFET directly with a motor or instead with relay + motor you need the flyback diode.
No. You haven't fixed the original problem, but your motor is now isolated from the rest of the circuit.
You've just now have a relay with an inductive element instead of a motor. Ultimately, you haven't solved anything (unless you are using an AC motor, and you don't have a triac or something else solid state to control the motor). You still need the flyback diode.
But you haven't doubled your problem by introducing a relay, merely moved the issue to another part.
Now - in regards to the mosfet - many mosfets (not all!) have a built in protection diode between the source and drain. Check your datasheet for details (including what kind of back-feed voltage/current can be handled by them - some may need an added diode with better ratings in detail).
EDIT: Also - some relays have built-in protection diodes (or can be ordered as such) as well (again, check the datasheet). You see this more on relays for automotive applications (ie - standard BOSCH style relays) than ordinary bare PCB relays.
A flyback is critical in anything involving a magnetic field, especially a collapsing magnetic field from a motor that stops spinning. The field collapse induces a relatively huge current which will be many many many times greater than anything a normal component is designed for.
Not having one is like driving your car down the highway without any breaks. The only way to stop is to crash.
Attempts to measure these spikes on a cheap scope years ago ended up blowing the scope input FET up. Whoops. Good job it was a university owned scope :D
Yeah - they make special high-voltage probes for this kind of thing (some can go up to 10 Kv and beyond - just depends on how much money you want to spend).
I believe that the main difference between a standard probe and an HV probe is one of resistance; I think the HV probe puts a large value (mega-ohm) resistor into the mix (not sure if it's in series, or between the probe input and ground - see my further note below).
If you have a scope, it's handy to have one around "just in case" if you can afford it. I got lucky myself; I found one for a few dollars at a local Goodwill thrift store (the strange stuff you can find there...)
Note:
Hmm - I decided to look a bit more into this - I guess things on HV probes can get complicated quickly!
https://www.repairfaq.org/sam/hvprobe.htm
So - a basic probe is just a voltage divider with large value resistors (like I alluded to earlier); but as the frequency increases, lots of other weird and fun stuff come into play (and in the comments section of that article, someone mentions special chemicals that had to be added to certain special probes he used in the past!).
Technically frequency compensation is required across all voltage dividers for scopes so not to accidentally create a low pass filter with the parasitic capacitance in the cables and input circuits. It's all quite fun.
Disclaimer: was an obsessive compulsive scope collector for a while.
Now think of all the electricity as one big wave. Cause that's what it is. If you were running 12v , you can see upwards of 30v surge. This is bad.
The key is to equalize the power on the motor. And that's done by putting a diode in the reverse flow across the terminals. So that big flow of electrons can equalize itself BEFORE hitting other silicon (like the MOSFET or your RasPi).
Ideally, you want to do this for motors, electromagnets, solenoids, and inductors(well, unless you're doing an L-based filter , but aside the point). They all have this magnetic energy->electricity->surge thing going for them.