We may be on roughly the same page but I think there are two definitions of "base" being presented here:
1) long slow miles, over hills maybe, no attention to pace, focus is on building mileage
2) tempo work, anaerobic threshold work, solid miles at aerobic threshold, light speed and hill work.
The issue is that 1 generally precedes and crosses over into 2 with younger athletes, athletes coming off an injury, or those building up to a new volume level over the previous year. So that leaves a lot of room for interpretation. And the reason I make that distinction is because you can't go straight to 2 or from 1 straight to interval work. In other words, no you don't want lactic sessions in the base phase, but you're not going to get there either by never coming close.
I think within definition 1, an athlete can and should do any of the following as long as they are unplanned and occur only when it feels right:
1) letting body dictate pace when athlete feels good as long as effort remains easy and controlled
2) throwing a few 15-30s surges onto the end of a run
3) finishing a run and doing a few relaxed strides (which shouldn't even be close to fast or long enough to stimulate phosphate utilization or require long amounts of rest)
But your suggestion that strides or hills needs an entirely different session after a 10 - 15 mile morning (which if you're doing that many on a non-long run day, you should probably be doubling anyway) is an idiosyncrasy, not a regimen that I've ever heard suggested in earnest.