A lot of this is solved by rolling abilities, especially if you don't let people move scores around.
In most of my campaigns we use a custom ability rolling method based on 1E Unearthed Arcana where you have a pool of dice to use. You can assign a certain number of dice to each stat but once you roll them that stat is fixed and you only can take the highest three dice for the score. That increases the possibility of a high roll in that stat, but also means bad luck equals a low number in that stat and you can't just move that number to a dump stat. This leads to a lot of variability in a lot of different areas.
I don't like heavy armor on my characters, but that is mostly because of its affect on stealth. We have a PC Cleric with a 6 dexterity in a game I am currently playing though and yes she has heavy armor (chainmail and shield). Beign able to get heavy armor and not having to take a -2 to AC is a boon. She is totally servicible as a Cleric too.