As interesting as this sounds in theory, most likely not. The balance would shift far too much depending on how effective someone's final smash is.
Like said before, the difference of effectiveness of the different FS could be balanced out by how fast it actually charge.
Final Smash Meter - Nintendo Direct 8/8/2018 (starts at 16:29)
Fortunately/Unfortunately the meter appears to build rather quickly. Most characters appears to complete the meter around 70% which is starting to get in to KO range for MANY characters.
I think it should be said that the balance WILL shift with Final Smashes. Some characters WILL have more powerful or useful Final Smashes than others. However, how is that different than what we have now? Characters already have different move-sets. Some characters are already competitively better than others, that's why we have character tiers.
The way I see it, with Final Smash Meter enabled in Competitive play, there will be two play styles or schools of thought:
Group 1: A character is picked based on their ability to acquire KOs outside of their Final Smash. Think Bayonetta, Fox, Sheik. Their move-sets will not require Final Smashes to be competitively viable.
Group 2: A character is picked based on their ability to acquire KOs using their Final Smash. Thinking of Mario, Jigglypuff in this case. Maybe they are currently mid-tier or lower, but with a strong tool like a Final Smash, they can be competitively viable but in a different way from Group 1.
On one hand, based solely off of the footage from the Direct, the meter may build too quickly to be fair. Characters that have outstanding or over-powered Final Smashes will be able to use them often enough. The kicker is that the meter builds when giving and RECEIVING damage, but that too is way to balance this mechanic.