There are 400 possibilities.
If you roll a 1 the 3 points ahead guy wins on any number.
2, same thing.
3, same thing.
4, 1 ties and highest dex goes first. Same thing.
5 needs a 2.
...
...
...
20 needs a 17.
Possibilities where you lose init: 20 + 20 + 20 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 = 264/400 = 66%.
Equal init = 50%.
Increased chance of losing init = +16%, or nearly one third higher.
Alternately, chance of winning init = 34% vs 50% or 1/3rd lower.
5% better chance of affecting whatever vs not having a 1/3rd greater chance to be bested by your equal. Hmmm...
And as stated you can get your saves to nat 20 only status without that.
Edit: I must say, it's nice to debate about something constructively, as opposed to the unnamed alternative.