That's why 4e only had point buy.Which shows the two breakdown cases quite clearly: either (1) you aren't actually strict about it, so the (arbitrary) bottom of the bell curve is cut off and usually power creep slowly raises what "the bottom of the bell curve" looks like, or (2) you keep these horrible numbers and almost always die, except in the rare cases where you get lucky. The former means abandoning true randomness (consider the rather complicated, and no longer all that random, default rolling method of 3e), while the latter means forcing players through repeated failure states before a success state appears. Neither is all that good today.
OSR games with modern design have found solutions, but even those have issues. DCC, frex, has the "character funnel": you skip over the process of waiting to get a character that survives by running a large number simultaneously through a meatgrinder. Any that survive thus already either have reasonably good stats, or have gotten lucky, and either option is generally acceptable. However, such things risk showing their gamist edge (after all, such a funnel is inherently dissociated, for anyone who cares about that sort of thing), and ultimately still devalue randomness by ensuring selective pressure that favors characters with actual bonuses.
Ultimately....I don't really know if there is a true solution to this problem. It very much seems like the two desired things--effective characters and easily-generated, truly random characters--are truly at odds. Being effective generally means falling in a certain range of power. Being truly random requires not falling in any particular range of power. Trimming the randomness to guarantee some competence either sacrifices simplicity and ease of use, or breaks the feeling of randomness, or (often) both.
I think, in the end, they either need to be just marked as distinct approaches with a warning label on the random-gen option, or D&D needs to decide which matters more. Because forcing the appearance of randomness while actually, in the end, forcing pretty non-random results is not really tenable long-term.