I usually eco pick. But sometimes (i.e. for certain kinds of licks etc) i find it (much) easier to strictly alt pick.

Is this a problem? Is there a reason I should stick to one exclusively?
No there isn't, both are useful in their own situations.
I prefer strict alternate picking all the time though.
Gear List:
B.C. Rich NT Jr. V (With Seymour Duncan AHB-1 Blackout in bridge)
Electro-Harmonix Metal Muff
Marshall MG15DFX
Jazz III picks
DR strings
Planet Waves Cables
As long as you are in control of switching between styles, it's fine.

Not sure what you mean by 'in control'. For a given lick, I cannot choose which I would rather do (well I can, but i'll be able to play much faster with one of the two). Are you saying I should be able to do both equally well in all situations???? You've just doubled my workload
Yes, it is very wrong and therefore you will die in an hour?

It can't hurt. See, people discuss technique too much. If it doesn't damage you, it feels good to you and you can use it to play stuff, do it.
Current gear:
Carvin CT6M
TC Electronics Dark Matter distortion
Harley Benton 2x12, with Celestion V30s
Laney Ironheart 60w tube amp