Op-amps, why do they have such low output currents
It's simple: manufacturers make what customers will buy! It's the same reason why Ferrari won't put a trailer attachment at the rear of their cars...

Price is a very important part of this, of course, and price is tied to silicon area, process, yield, and of course packaging.

For example, an opamp with +/-12V supplies and 1A output current will dissipate several watts, so it can't be a standard opamp package like SO-8. Thus its target audience shrinks down to customers who are willing to use this specific package, which won't be standard so there won't be a second source in case the first manufacturer is out of stock. Also the non-standard package means it can't be marketed to customers who want a standard opamp, unless it's something like a SO-8 with a thermal pad, which has its own sets of issues, it's a lot worse thermally than TO-220-5 LM1875 for example.

Contrast this with, say, a NE5532. In the unlikely case it's out of stock, there are tons of equivalents. Package is standard... it's a jellybean part.

We haven't gotten into actual tech limitations yet, and already the economics favor the chip that will cater to the largest audience, in this case small signal, low current circuits. Even if the thermally enhanced package adds only 5c to the cost of the beefier opamp, it's 5c too much if you don't need the capability.

Now, higher output current requires larger output transistors, thus more silicon area: it will be more expensive. It will also be slower.

Say you make an ADA4898, top of the line, ultra-everything opamp. The process for that is likely to be damn expensive, also all the chips that fail the stringent spec tests are trashed, so yield can be an issue. The folks at AD aren't going to enlarge the output transistors if this only interests 5% of the customers for this product... because this would make it more expensive for the others, so they'd pick another opamp...

Maybe the manufacturers can't do it? Well, nope. If there is a market, they will rush into it. Check ADA4311 for example, it's a driver for PLC/DSL/Whatever twisted pair, it's fast, low noise, high current, etc. But it's a current feedback amp with high offset and crummy DC specs because these don't matter to the application, so going for a precision design would only increase cost.

Now check LM1875, an audio power opamp. It's old, crummy and slow, so it can be probably be manufactured on a cheap old process with high yield. It could be better, sure... but it's good enough for the application.

If you want an opamp with good small-signal specs (DC offset, noise, etc) and high current drive, the simplest is to stick a power output stage on it, or make a compound with the first opamp driving a beefier one. If the second opamp is faster, no extra compensation is required. If it is slower, compensation is required.