Ive played D&D, 1E AD&D, 2E AD&D, 3E D&D, 3.5 D&D, 4E D&D and now Im playing 5E D&D. Following is just my opinion and in no way am I saying anyone who disagrees is wrong or I am right its just based on my observations over the years.
When we played D&D, 1E AD&D, 2E AD&D some DMs were more lenient and flexible as to how they let you roll and assign your ability scores, others were not so forgiving. One thing was always pretty constant, that was that the first thing you did when creating a character was to roll your ability scores. Hands down this dictated what type of character you could make based on race and class requirements. People I played with generally accepted this and played whatever character they created from what they had to work with, tried to keep them alive for the sake of the campaign, and if you did die you started from scratch again. On the rare occasion when you rolled really well and got that really awesome character you made sure you did your best to keep them alive. Twice I can remember getting one really great roll for my character; I had a fighter with 18/00 STR. I rolled for exceptional strength and before I could look down my DM said "HOLY S**T if I didnt see it I wouldnt have believed it". The other time I was playing an Elf Wizard/Fighter/Thief and some circumstance occurred that I could roll for a psionic wild talent, I ended up with the pretty lame ectoplasmic form. That same character at 4th level took out a stone golem single-handedly as my cowardly compatriots ran and hid. There was nothing particularly special about that character so I think it just goes to show that you can do some pretty great things with average characters.
With 3E and editions after where players for the most part can play whatever character that they want, I think that feeling of ending up with a really special character that you really cherished has somewhat fallen to the wayside, especially with players who never played the earlier editions. I think that if the original poster has a specific campaign vision in mind and makes it clear that hes going to put some limitations on character creation (regardless of what those are), as long as the DM is fair and his players respect and trust them, then you'll probably have a great game; one their players may appreciate.