Oh I totally oversimplified it. In the Scotch world they can use many tools to get the profile they want. The malt, the roasting of the malt, the yeast, the distillation cuts, water/ABV%, the barrels chosen, the length of aging etc. Lagavulin and Caol Ila start with identical malt from the same roaster, roasted to the same specifications. So the profile differences come after that.
Scotch is such a diverse product. The low end (JW Red), you've got a young blend, with a lot of grain rather than malt, and not much age. It's not very "smooth", not because it's "bold' and flavorful but because it's cheap, it's a lesser product. Then you get the inexpensive base single malt expressions, like Glenfiiddich 12, Glenlivet 12 that are in ex-bourbon. Those are lower proof 40%-43% and are pretty smooth and approachable. Then you've got the same, but peated or partially peated, something like Caol Ila 12, Talisker 10, Laphoaig 10, Ardbeg 10. Or you've got upeated, but Sherry cask, like Glendronach 12, Macallan 12, Tamdhu. A few like Hazelburn and Tobermory go in a different direction, and use the cuts and yeast to give their base expression a notable funk that is quite different from something like Glenmorangie 10. Then things get wild, as you go to cask strength independent bottlings, wine/port cask stuff, etc. Even with sherry cask, Genfarclas is known to reuse those casks many times, the sherry influence is muted. Others use first fill sherry casks, and the influence is very strong. Same happens with ex-bourbon barrels. So you can create very unique things. Then was it "finished" or fully matured in sherry, wine/port? Big difference there as well. Prices will climb with all those elements plus proof. But prices also climb for super smooth and frankly bland stuff like JW Blue.
Lagavulin 16 is pretty aggressively peated, lots of smoke, but then they water it down to 43% and age it 16 years in ex-bourbon, which cuts the peat down. It's a pretty damn dialed in product, which is approachable and "smooth", yet has more flavor than a regular base unpeated Speyside.
As for aging after bottling, there isn't any real benefit. That pricing is likely just scarcity. People are interested in trying something made long ago. I mentioned trying old JW Red for example, it was far better than the modern stuff. I also had a bottle of Cognac VSOP from 1969. Tried side by side with the same product today, there is no comparison. The older one was clearly aged much longer before they bottled it.