Whopity, that's what I understood too. What is commonly referred to as a "frozen ATPL" is just a CPL+MCC+IR+ME+Type Rating+all ATPL theory exams passed. But technically it's just a CPL.
You use that to build your hours and once you get to a certain number (I thought 1500? But it might be 500 too.) the whole lot is converted ("unfrozen") into an ATPL.
So yes, with a CPL you can fly RHS of an airliner but if it's just a CPL you have no hope of ever becoming the captain, and without that outlook there's not a lot of airlines that will take you on board.
So if your intention is to become a career pilot, then an ATPL is virtually the only viable option. However, I know quite a few guys (and girls) who only have a CPL and do various odd jobs next to their main (non-aviation) job, and are having a tremendous time. Flight instruction is of course the biggest example, but also a lot of banner towing, parachute dropping, sightseeing flights and so forth are done by people with just a CPL. And they got that CPL, amongst other reasons, so they didn't have to 'cost share' every time but could get their flying, at the very least, reimbursed fully. And maybe make some money to pay for the trip to the airfield and the beer afterwards.