We have different ideas about what constitutes "nigh-unplayable," buzz - when I read posts about three or four round 3e combats that take an hour to resolve, or of 3e dungeon masters using egg or chess timers to speed up getting each player's actions completed, that fits my definition of "nigh-unplayable."
The 1e AD&D initiative rules are actually very simple: high roll wins, ties are simultaneous. Weapon speed factors come into play in a battle with another opponent armed with a weapon, or a spell-caster - in fact one can spend an entire evening battling dozens of monsters without ever calling upon the speed factor rules at all. In the case of opponents with a weapon, speed factors resolve initiative ties (which involves the terribly complex calculation of comparing two numbers to see who wins...) or open up the possibility of getting in one or two attacks before the opponent could strike (which meant that most characters and weapon-wielding monsters used faster weapons - not too many pikes or zweihänders in our dungeons).
The only time that this became even a little complex was with respect to spell-casters, which involved comparing weapon speed factor and casting time to the initiative roll. Do it a half-dozen times and it becomes second-nature - you'll never find yourself spending more than a few seconds on it again.
With these rules in mind, players and dungeon masters adjusted their combat tactics accordingly: if you want to take out spell-casters, use a light weapon like a short sword or dagger, and if you're a spell-caster, employ spells that only take a segment or two cast (or better yet, use a wand). It wasn't like we were switching weapons constantly and having to look up speed factors every time we threw down with an evil cleric. It was part of the (wait for it...) TACTICAL element of 1e combat.