Usually soldiers die quickly, so I understand that reaction fire is used tactically... I dont think it is a huge problem per se, because you try to be cautious and not end up losing all soldiers.
As far as the advancing is concerned, perhaps there should be ways for inreased movement rates... just throwing a wild idea, dont worry about implementing it at all - it could be kinda cool if soldiers really run as fast as possible to reach some cover or other area, afterwards they are so exhausted that they cant shoot or move for some time (or shoot only like 1 shot... or just have decreased movement rate for the next ~3 turns)
This way a part of the squad could try to quickly change cover running, while the other part covers and protects them... Anyway, i am just throwing a wild idea here, dont bother too much shooting it down
Perhaps also have the option to have the option of a wider overwatch field of vision but at the expense of range, so it takes into account if soldiers are pinpointed on a certain area or looking all around at different areas and so wouldnt be able to traverse guns so easier at a specific area.
I think this idea might have merit... for example the soldier could notice the area in front of him, but at the expense of noticing anything else... he could get a small bonus for that area he is surveying, but really does not notice anything else at all.... Although I am not sure that this would be worth to see improved, it might make the game a bit more complicated... perhaps it would be better to discuss this idea some time later?