It depends what you mean by "refurbishing"; each element is different.
The solid rocket boosters, for example, suffered a hard impact into salt water. They then had to be fished out of the water. And of course you don't just "refill" a SRB, they have to be taken apart and recast, then put back together.
The ET is disposable, and had to be rebuilt from scratch.
The orbiter was legitimately reusable, but with design flaws.
I don't blame the shuttle program - they were sort of pigeonholed into this dead end by circumstances. The concept came about during the heyday of the Apollo Programme, when NASA budgets were serious. It was supposed to be a much more reusable, much more maintainable, and somewhat smaller system. It was supposed to then have a huge flight rate supporting all of these big projects that were on NASA's docket, including a permanent moon base and a huge manned orbital station dwarfing ISS, which was supposed to replace Skylab.
But of course, Vietnam and the realities of having soundly trounced the USSR in the space race led to their budgets being slashed, which pushed the program into ever more untenable positions until it was nothing more than a jobs programme. Forget full flyback reusability of all parts. Forget the titanium frame for the shuttle, which would have let it run hot and thus not required so sensitive of a TPS. Go begging for money and be forced to modify the design to meet Air Force requirements, pushing you into an inferior design position. On and on.
If I'd fault them for anything, it'd be for going straight for a full reusable workhorse rather than a small-scale pilot programme first. But those were the days of optimism. Optimism which only recently seems to start being regained.
Either way, the Falcon boosters are a very different beast. A vertical soft landing is hugely different from the SRBs, yet the thermal issues are far easier than with the Shuttle. And the Merlins were designed from the start under the principle of preventing the need for a full teardown. That doesn't mean that they will be cheap to reuse. But it does mean that they have the possibility of it.
I do think SpaceX had a rather clever strategy, in that while their goal was reusable, they made a rocket that in the process was cheap as a disposable. So they could get volume and flight history while working on getting the kinks out. They may have flown too close to the sun with the densified propellants and (externally) unlined COPVs, but obviously, with a company like this, their whole existence is to push the envelope.