How large an area is needed to make a paint sprayer worth it?
This is one of those questions that really doesn't have a good answer.  I will comment on a couple of aspects.

A good quality airless sprayer is expensive. Even a basic model can cost $300 or more. A good pro model is $500 plus.

The small paint in the head types are iffy at best and don't do a good job if tilted at any severe angle, like when doing ceilings.  They are also very loud, vibrate a lot in your hand and are fatiguing to use. They typically only hold a pint to a quart of paint. 

A good high pressure airless sprayer takes paint directly from the can 1 or 5 gal, and has hoses, 25ft to 50ft to the spray head. They also have interchangeable nozzles for different types of paints and stains and to control spray width. 

If you are only doing a few rooms, I doubt it would be worth the investment to purchase one.  You may consider renting if the job is large enough.

Keep in mind, even though you can spray out a room or even do a whole house very fast with a sprayer, you still should over brush or roll to get a good finish. It does take some practice to get the feel of using a sprayer. I use one often and absolutely love it. I always have a second person to over roll immediately while the paint or primer is wet. It is extremely effective shooting PVA primer on new sheetrock before trim and floor coverings are are installed.