Did you mean "Shouldn't be able to move more then 3 squares from a city or colony"? I'm going to assume so since otherwise your post makes no sense.
While that would be an interesting variant, that would cripple the expansion of most civs early on. A common opening strategy is to explore around the area with your early units to find the best city sites and grab up the goody huts. Exploring allows you to find your neighbors (and kill them!) faster, which *ahem* allows for earlier trade (Really! Trade, not death dealing...). Changing that facet of the game would give a bonus to civs that don't rely on early trade as much for tech growth. Also, limiting it to military units would give expansionist civs too much advantage as well (presumably scouts could travel wherever they want).
It would also make warfare pretty much impossible except against cities that directly abut your own.
I could actually see something like this working, but maybe not limit it to the units, but to the government? Perhaps just despotism has this limit? Maybe come up with some idea where the number of units you pay for support rather then simply support wth cities would be the number you could operate outside your cultural boundaries? That would make some sense. IIRC, Civ2 had something similar though (been awhile so my memory's foggy). You're units had a home city that suported them. This didn't affect where they could go, but they cost money to support if they were outside their home city. I'm sure some variation of this could be introduced, but I don't see it as adding that much to the game (cept to make things slower earlier on).
Heh. Part of me likes the idea, but part doesn't. I just think it would make cifilizations too much like islands. The interaction and threat of invasion at any time is part of what makes the game more challenging IMO. Not allowing any real invasion of other civs until the modern era would be a bit much I think...