Longbowmen have a better melee attack than ranged. Assuming the shield bug is patched, they will soon be much better at hand-to-hand.
Melee exposes them to more losses so it's still a last resort, but last resorts are important. Many times, I've sent Desert Archers and/or javelinmen into melee when a regular infantry unit in front of them was wavering. These new troops restored morale and saved the day almost every time, in MTW1 and 2.
Although archers can't catch routing units as well in MTW2 as they did in 1, they can "keep up the scare," making a routing unit run farther before recovering. They can also stop periodically and shoot the routers in the back. Get 'em running, keep 'em running. Then they can turn around and shoot into the backs of units that haven't routed yet.
About the only English missile troops I've never send into melee are peasant or militia.
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It's hard to get crossfire going with foot troops, but any unit caught in crossfire by longbows would quickly become mincemeat.
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