Engine rebuilds are still common among British sports car folks, as the engines aren't being made anymore.
I've been back and forth on an MGA here locally that has the engine in pieces. The machining on the block and head has been done, but is old enough that they will both at least need a dip. If I buy it, I'm going to have to get a crankshaft, pistons, and connecting rods(along with the other staples like the camshaft and main bearings). There are tempting-and plentiful-engine swaps available for it that are more or less drop in. The 1800 5-main engine from the MGB and a lot of other not-so-common-in-America cars is one such engine, but I want the original 1500cc 3-main engine. These aren't so plentiful.
At the same time, not too long ago my local MG mechanic had a lady bring in her daily driver '77 B a few months back with a blown head gasket. After pulling the head, he found enough issues that(after talking to the owner) he ended up just dropping in an engine he had sitting on the shelf. It was faster, cheaper, and easier than fixing the head on the old one. I've said something to him about buying the one he pulled to do something fun with it(probably skim the head, have it ported and polished, put higher compression pistons in, a mild street cam, and then find a nice roller to put it in).
On the other hand, if I needed an engine for my daily driver Lincoln, I'd be on the phone with every pick-and-pull in a 200 mile radius(I probably wouldn't have to go that far). Chances are, that would be cheaper than even doing a head gasket. Fortunately, it's not a particularly troublesome engine and has been looked after well in my care. It's about to roll over 150K, and has no signs of showing down.