How about place the 16 where you want it, then roll 3d6 in order?
So I'm guessing you've played since at least 2nd edition?
My beef with rolling has always been the random. In the earliest editions, ability scores barely effected combat. For example, in 2nd edition a strength of 16 gave no melee hit bonus and a +1 damage bonus. Other ability scores were similar. Wizards spells were the same regardless of intelligence score. Combat was essentially determined by level and class. Ability scores mainly effected skill checks and other outside-of-combat things.
Rolling in present edition means thats some characters will necessarily be more powerful than others. If you roll well in one fight your character outshines the party in that one fight. If you roll well in character creation you will outshine the party for the entire campaign. Sure that character could die at some point, but when the solution to a problem is killing off a PC, it would probably have been better to nip that problem in the bud.
Rolling a poor character is even worse. A few people might get excited at the idea of playing a sub-optimal character, but I personally find it gets old after a few sessions.
If you and your party are comfortable with rolling and enjoy it, go for it. Keep in mind that a character with lower stats compares to a lower level monster, higher stats to higher level monster.
My ideal solution would be to separate the ability scores from the attacks/defenses. Most characters have a primary ability (for attacks) and two secondaries (for effects). I would let them choose from a set of pre-determined bonuses to these effects such as 5/2/1, 4/4/1, 4/3/3...
For example the rogue choose 4/4/1 and apply +4 to dex attacks, +4 to strength based effects and +1 to cha based effects, without having to take the exact stat blocks that match it. The upside to this would be that players no longer need to have stat blocks like this to be optimal
18
10
18
8
10
14
but holy crap, this is another rant for another thread...