You clearly have not read the appropriate NASA documents.
Actually, yes, I have.
Skylab was in very good condition and NASA wanted to use it in conjunction with the shuttle
NASA was (is) an organization of thousands of people - and cannot "want" anything. A small group of people, who had no funding, wanted to use Skylab in conjunction with the Shuttle, but that was just one of the dozens (hundreds?) of pie-in-the-sky ideas various groups within NASA generate on an annual basis. Very few space fanboys realize this and presume every single dammed one of those gotta-publish-something-to-keep-my-job studies and "plans" (was) is something "NASA wanted to do" no matter how ludicrous the idea was. Actually, the more ludicrous the idea the more the space fanboys love it, because it's just more ammo for their ignorant whinging about NASA's "failures". Ignorant because on top of not grasping the pie-in-the-sky nature of many of those "plans", they fail to realize that NASA is not an independent organism - but rather is a branch of the Executive Department and only does what the Executive approves and Congress fails.
Congress did not fund this cheap solution, so we ended-up dumping $100 Billion and ten years of construction time into building ISS to get a similar orbital capability (Skylab had 320 cubic meters pressurized volume, that's more than the US part of the ISS).
What's interesting here is you claim Skylab would provide similar capability - but then rather than comparing capability, you compare volume. Thus, probably inadvertently due to gross ignorance, you reveal the shallowness of your knowledge. In reality, Skylab didn't have a fraction of *any* of the capabilities of the ISS. It doesn't produce as much power, could only support a much smaller crew, and wasn't equipped with but a fraction of the scientific equipment, etc... (Even though Skylab and the ISS have a similar volume, the ISS has almost six times the mass. There's a reason for that.) Nor, given the small diameter of it's hatches, could it have been reasonably refitted to provide significant extended capability. Raw volume is impressive, but it's no more useful than an empty house. It's useful stuff that make a house or a space station useful, and Skylab was grossly lacking in that department.
The shuttle could have then flown additions to Skylab (which had a docking adapter for multiple visiting vehicles).
Yes, Skylab had a docking adapter for visiting vehicles. No, they weren't useful for adding additional modules. On top of lacking the structural strength, they had no provision for routing power, life support, data, etc. (Not without running cables through the already narrow docking tunnel - not that there was anywhere to hook them to on the Skylab end anyhow.)
When Skylab re-entered the atmosphere it did so under remote control from the ground, with its systems fully functioning until they were destroyed by the reentry.
No, they weren't "fully functioning". The third crew had to use a lashed up servicing system to replenish the freon loops in the air lock module (which were leaking). The also had to perform a spacewalk to install a back up set of rate gyros since the original set were failing. (Etc... etc...) Skylab was worn out, and it's equipment was beginning to fail even while the manned occupancy program was in progress.
A lot of people believe that Skylab was some lunar landing level program, and that in the same vein "tossing it aside" represented the loss of some grand capability. Nothing could be further from the truth. Skylab was a shoestring budget program subsisting on Apollo's leftovers and discards. (To the point where they had to take a hatch off an unused Gemini to provide an EVA hatch - they had no money to develop or build one of their own.) It had a minimal lifespan and modest scientific capability with no capacity for significant resupply, replenishment, refitting or extension.