Running a sprinker line under a concrete footer?

the contractor, of course, is giving you the cheapest, fastest solution.  will it last?  probably for years, yes.  will the concrete crush the line?  no -- concrete shrinks as it dries; crushing would only happen if it expands

not sure why a patio needs a footer unless the soil is that unstable where you live, they are always just a slab where I live

the line will be fine as long as you drain them properly before winter sets in but if something were to happen to it then you would need to reroute it around the patio because even if you put it in a sleeve ground water will seep into it carrying dirt and locking it in there and making it impossible to run another pipe through it 10 years from now

it should be completely rerouted around the patio

I would have him install a piece of ABS pipe under the concrete as a conduit for the sprinkler line to reside in so it can be replaced if needed.

You're not wrong, then again why anyone would waste money watering their lawn is beyond me.  If your plants can't survive where you are, spend your money on plants that will, rather than continually spending money trying to keep plants that won't.  My way, you spend once and you're done.  

I'd shoot for the continuous piece if I had no choice, but my choice would be to pull the sprinkler line and never look back.

if it goes under concrete it should be inside of a larger pipe so if some thing goes wrong it can be easily replaced  

I would replace the line and house it in a plastic duct such as rainwater down pipe. That way you can withdraw it and replace it if necessary.