In Edge of Tomorrow, once Cage knows the location (and time of arrival) of the original Alpha that gave him his powers, why can't he arrange for others (or at least Rita Vrataski) to be there when it comes, blow it up, and get it's blood to gain the ability as well - wouldn't it be better to have a small army of time 'travelers'?
Wild speculation. Since the mimic is a hive mind that the Omega is controlling, perhaps when the Omega rolls things back, they change things up a bit to prevent the Alpha death? So you couldn't depend on the Alpha reliably being in the same place, or being vulnerable to the same attack.
For one thing, Cage doesn't want to get killed by an Alpha, they can take his power away from him. So he's going to be steering clear.
As for someone like Rita, she doesn't know what to expect, she doesn't get dozens of tries. She only has one chance, the same chance every time, to get to the Alpha and not get killed along the way. And consider how hard it was to get to the Alpha in the first place, how hard it would be to repeat those same conditions with someone who's never been there before.
Plus, she probably doesn't trust Cage to shoot himself when she dies, so she's not going to let him out of her sight. So the best option is to have them both go in and avoid the Mimics as much as possible.