I'm discussing point buy versus the rolling option in the PHB. The PHB doesn't have a minimum values it just states "Random Generation. Roll four d6s and record the total of the highest three dice. Do this five more times, so you have six numbers."
You may not force a player to play the character with low numbers, the rules don't mention it. I've also been in games where one person rolled incredibly high, another rolled incredibly low. The DM literally laughed when the person rolling low asked to roll again or use point buy. Maybe most DMs don't actually use the rules as written when rolling for stats I'm talking about the rules from the book.
As a sanity check, I went to Random.org and generated a list of enough numbers from 1-6 for 9 tables to roll 4d6 6 times. I then sorted the results in groups of 4, got rid of the lowest number in each set of 4 and came up with ability scores. Thank goodness for macros and excel. Probably didn't need to bother generating as many numbers as I did because the very first group was
1) 11, 17, 5, 18, 12, 10
2) 12, 12, 10, 8, 17, 12
3) 10, 12, 10, 5, 15, 14
4) 8, 6, 12, 12, 13, 9
5) 16, 12, 13, 14, 10, 11
6) 15, 12, 14, 13, 9, 14
Depending on preferences, more than one of these characters are fine. But #4 with 8, 6, 12, 12, 13, 9? They're way behind the curve when one of the other players could start with a 20 as their primary stat and an 18 as their secondary or start with an 18 and nothing below a 10.
This wasn't out of a thousand groups, this was literally the first group in the list. It's not the difference of the primary stat being +/- 1, it's significantly lower numbers and #4 will be noticeably less effective from a numbers perspective as the rest of the group. Some people may want that, I don't.
Ah well, I really need to stop procrastinating and I need to get some honey-dos done.