LCCs encourage their passengers to take out insurance as protection against cancellation delay etc for which they will not accept any responsibility. They have moved a cost burden from one industry to another.

I wonder if travel insurance premiums have been affected as a result of this trend?

All airlines encourage passengers to take out travel insurance to cover delays out of the control of the airline, out of pocket expenses and missing / lost luggage.

Unfortunately most people don't get insurance and expect the airline to cough up for everything.

All airlines have limits on what they pay and that is listed in the T&C's. Its not specific to LCC's only.