Maybe a little bit. But I think it is more that it is a material with heavy atomic nuclei and high density, and thus effective at blocking radiation. And it is also relatively cheap.
They used to talk about using barium cement but it just can't compete, price-wise.
I think >80% of the current industrial use of lead is for batteries. It's probably still in the top ten most mined metals by dollar value and definitely by mass.
Aluminium, was so expensive until the Hall/(that other guy) process was developed, that it was used for jewellery [1]. It's expensive and difficult to reduce Al ore to metal, which is a supply side problem.
The economy sort of has a "working capital" quantum of aluminium which also grows steadily from aluminium mining.
Lots of metals have very different and complex supply structures and thus completely different $$$ / volume curves for their supply.
Understanding the $$$ / volume curve of commodities is not something that is commonly considered when people try and predict the future. Mining a billion tonnes of Aluminium from an asteroid for example and safely landing it on Earth can never be profitable because the $$$ / volume curve for Aluminium is $0.00 at billion tonne volume.
Lead is still routinely used in many applications today, either in metallic form, from ICE car batteries, to fishing or hunting gear, or as chemical compound in different kinds of glass. And the same can be said about other heavy metals like Cadmium or Mercury. Industries also routinely work with much more nasty things than lead, so it really doesn't sound like a show-stopper.