I see a lot of disregard for the Cossack unit. IMO, it is one of the most deadly units out there, because of its speed and blitz. I think the reason you undervalue them is because you're thinking of them as an offensive unit. They're not really: they're tremendous defenders! I'm a builder. I don't start many wars, and when I get into one, I'm usually outnumbered3-1 or worse. But if I have Cossacks, you're doomed. First, my territory is always well-roaded. So, I zip up to the border, cross, pillage, and retreat. Now, you have no roads going up to my border, nor away so you can't leave and heal. Anything that crosses into my territory, never gets back out, a la Napoleon in Russia. I get to raid your reinforcing units, and your redlined units, then withdraw back to town. They don't have great defensive strenths, so they are usually the last to get attacked in my stack. I hate when my cavalry gets attacked, when I have unengaged inf in the stack. I want my cav to be held back for counter-attacks. If the enemy sends a lot of attackers, the blitz is very useful. It means that I don't have to have as many units built and maintained to defend myself prior to outbreak of hostilities. The great thing is that the Cossack can move, attack, blitz, then return to town to be healed, and be ready to go 2 turns later (assuming a barracks). As was pointed out, they get promoted rapidly, so they can be built in a town sans barracks, while you use the towns with barracks to build your inf. Because they have a move of 3, they can go 2 tiles per turn in the hills. They can cross the border in a stack after I've whittled your army down, and hit your town that would be out of reach of most units. In a really large stack, they're almost unparalleled in a first-strike action. Move 'em up to the border, declare war, and take an enemy town right off the bat. If you have your garrisons on the border, too, when you take that town, you can immediately garrison it by moving down the road with your inf. If you hit the middle of his border cities, then almost all his follow-up movement and attacks will head right for the strength of your army. The little that leaks across your border can be handled by the couple units left to garrison your border cities. I have literally driven straight down the middle of an opponent's nation using this tactic. Strike from beyond the border, move in the inf, consolidate. Repeat as necessary.
The overlooked thing about Roman legions, is that they do double duty. They're strong attackers, so the AI is less likely to pick a fight with you, and they're strong defenders. Basically, they cost the same to maintain as workers, do road building, build border forts, and allow you to maintain a larger army during peacetime. During wartime, they go fight, at a time when your workers have to flee the border regions. Instead of using your pop to build workers, you can instead build settlers. Conquered territory is easily re-roaded, and new border forts built, by the stack of victorious units left you at war's end. As the Roman player, what you take, you can hold: just build roads and forts!