I believe many european ATC units do not have access to primary anymore, certainly the case in germany as far as i know.
Anyway, yes, it is a very good idea to keep some lookout, especially in airspace that might have mixed use, mostly below FL100 in europe. And even during cruise, but mainly for weather avoidance. For traffic avoidance it is bloody useless, as most human beings cannot judge relative altitude worth a dime up there. Not to mention that transponders are a requirement, otherwise you won't be up there. And that TCAS is as well, well, for airline flying anyway. Yes, TCAS may be inop up to three days, but in my experience it is a very reliable piece of equipment, in 17 or so years of airline flying i had one failed TCAS, and it was repaired during the next nightstop.
Just checked our OM/A, no requirement for lookout during cruise, but a requirement to check weather via WX-radar and reports via ACARS.