I recently started testing builds with no boots (running warlords for sustain and move speed quints and wanderers mastery to make up the difference). Before you completely shut this idea down, at level 1 I've got 355 move speed (out of combat) and after picking up a zeal item I make it to 371 which puts me more or less on par with tier 2 boots. In combat, I'm relying on crits to move around, so its really a question of map mobility and I would argue I can get to an acceptable level of movement speed; nothing super major (certainly no quinn) but fast enough.
Now, the build would have an infinite edge, essance reaver, phantom dancer, trinity force, Lord dominiks, and a blood thirster. This plus a red pot (or w/e that attack potion is) gets you to an even 850 AD, 100% crit chance, max cdr, idr now much move speed on crit, and has you sitting at around 390 ms before you crit (and apply phage proc). Statwise, this is the best I think you can do; I realize now I forgot to check a second phantom dancer (that might result in more ad than then trinity force) but I would argue that the benefits the trinity force gives you (slightly more health, sheen proc, and more movement speed) makes up for it.
Of course, I would say that the life steal item could change depending on the team you were playing against; it might be more beneficial to have a maw or, like you pointed out, a scimitar depending on the team you were playing against. But in an ideal game where you don't have much to worry about, I think my build is the strongest stat wise. What items to build when, however, can be a little tricky and I have only just started to test this out so I don't have enough games with this yet to see how the builds tend to work.
