You are playing fire. What is the counter to a devonion dragon (10/5)?
If you said rage potion, that was a good guess, but I have upgraded this dragon to a 10/6 dragon for that exact reason. The correct answer was explosion to remove the pillars so that I couldn't get the dragon out.
Every card has a counter, and sometimes that means not letting it hit the field safely (what are you going to do about a phase dragon? try to keep the 13 aether quanta from being available, that's what).
Most creatures aren't like that, but some are. If we can customize creatures as you suggest, it changes the counter based on how much and what was upgraded.
I don't want to think of deathstalkers or dune scorpions with 1 attack, bypassing the check for their poison. Maxwell's demon can help keep fireflies in check...unless they are 3/3 (4/4 upgraded), which then renders them immune to paradox.
Then we have a situation with mutations. Why don't I just upgrade to a 100/100 light dragon. The moment I get one from improving skeletons, the game is over.
Why don't I throw in fate eggs for good measure, as well?
Certainly you can see the problems with changing creatures like this with regards to countering those creatures, and what it would do to the balance of the game.