freeD6 down the line

Lately, I've been convinced that the most useful part of stats is in providing a prompt for you to narratize, and the least useful part is as passive bonuses or interaction buttons. Does an item on your character sheet need to do anything other than that? Millions of people using alignment in 5e say yes. We can go further even than OD&D str/int/wis. We can make ability scores entirely vestigial.

 Here's how you roll ability scores, now:

1. Declare what you're about to roll. It could be strength, or dexterity, or charisma, or your relationship with your mother, or your place on the left-right political spectrum. Anything that fits on a bell curve if you squint. Make sure you declare what high and low are if you haven't already ("left-wing is high, right-wing is low" or whatever.)

2. Roll 3d6 for that score.

3. Repeat as often as you feel like, but no backsies on what you already rolled.

Even if you choose to employ these for bonuses somewhere down the line, this is a balanced method, since you're as likely to be screwed on something as you are to benefit from it. Most importantly, it's simple and fun, which is good if you like high lethality. It also combines well with high lethality because you get some good variety in who you play - a sort of intensification of the virtues of traditional 3d6 down the line.

This may require some clarification about what the average looks like, but if so, that's an opportunity to get on the same page. If I declare I'm rolling "how often they get in trouble with the law" and roll an 11, then we can converse and get a consensus (or dictat from behind the GM's screen) about whether this is a setting where the average person is harassed by the local authorities or basically doesn't interact with them, and so on.

Variations

1. Combine with it takes a village.

2. Pass it around. Create characters as a group and declare what the person to your right is rolling for. 

3. If it's one person rolling up a replacement PC, let everyone contribute one stat.

4. Roll first, then go through this choices-based system.