Yes rally cars need to pass the mot, our punto will pass again if we spend enough on it but we will be getting a new car to replace it anyway.
I think the point is, if you're happy to spend a lot of money on the car to keep getting it through an MOT then why not just pay the money and carry on using the car as before.
If you want a rally car then you may be better using a better base, if there is one thing everyone on this forum will tell you, once a fiat (especially a punto) has the dreaded tin worm, you'll spend your life chasing the rust with a welding torch, and we all know what kills puntos is rust.
The other issue is the punto doesn't lend itself well to engine swaps. Its a fairly small engine bay so shoe-horning a different engine in, can require a lot of work and skill. Depending which model of punto it is, you may find it more cost effective to find a Punto with an already powerful engine, something like the 1.8 HGT in the older mk2 and mk2b cars or an Abarth model in the Grande and Evo. which would not have the rust problems of the older Mk2 models. a proper Engine swap can cost thousands.
It's always a nice idea but often the practicalities are just not there.
If you have a bit of land, you can hoon around it in it till the wheel fall off, that's probably the best and most appropriate use of an old punto which has reached the end of its life and won't pass its next MOT.