Just opinion, to be taken with the usual grain of salt. As modern aluminum electrolytics have become smaller and have lower dissipation factor (I never talk about esr unless talking about switchers), the need for tantalums has shrunk.
Looking at the positive side, tantalum caps have moderately low dissipation factor, but it's also very consistent. Low, but not so low as to cause ringing. A designer knows that every unit will operate within narrow specs, even if the vendors are different. Tantalum caps last near to forever; when recapping you'd never change them for new tantalums unless there were a problem or history of problems for that unit/type.
On the negative side, the tendency for short circuit failures is well documented. IMO, tantalums of any vintage have no place in non-current limited locations. If a short circuit will cause high current consumption and start a fire or char the PCB, it's a bad design.
I'm lucky enough to have a vector impedance meter and can look at caps as high as 110 MHz. As far as I can tell, the HF benefits of tantalum caps are mostly myth. Lead length is the killer up there and any cap with leads is going to perform poorly. SMT is the way to go. At more reasonable frequencies I haven't seen a place where a modern low dissipation factor aluminum cap won't replace a tantalum just fine. Maybe they exist, as National Instruments was always very specific about using a small tantalum or large aluminum electrolytic to bypass their regulators, but I can't confirm it.
If you look at the residual signal across a tantalum cap, it's pretty awful. They make horrible integrators and you'd never put them in the signal path, series, shunted or any other way. Even where the audio signal across the cap is very small, say in a coupling cap, I wouldn't use one.