They're a rough approximation compared to carrying through both accuracy and precision information and doing a full error analysis. Most of the time they're good enough, but sometimes you really do need to know that. EG some widget is 56mm +3µm/-500µm, that's very different from just saying it's 56mm. Significant figures ignore the actual error distribution.
Since I made the point, I'll also argue that it's often not relevant. Most of the time the particular error distribution doesn't matter, and significant figures are a good enough approximation. The biggest issue most people have with them is that they're first taught in high-school chemistry class, and they're not taught error analysis first. Significant figures are then seen as difficult complications compared to just copying down what your calculator outputs, instead of a simplified approximation compared to the work needed to do a full error analysis. Sig figs thus get seen as something difficult and harder than the default, rather than as an easier shortcut than the default.
Also most calculators and unit converters don't take them into account by default (or at all) since someone might actually have accurate tolerance information to do a full analysis.
FWIW in my field of web performance I'll follow, and ask others to follow, simplified significant figure rules. For instance I'll see people copy down +1.5785% +- 0.10345% improvement. In which case +1.6% +- 0.1% is a better presentation.
In think the CS industry and the tooling like you mention should do a better job here.