Adam,
Are you arguing against 3 shots, or the term 3 "full" shots? The former is the definition of par, I think, even if the lengths used on the USGA rating system never increased with distance gains.
As to the main question, there are two problems in designing par 5's IMHO.
First is that the middle shot is inherently less interesting than either a tee shot for positioning or approach shot. Unless of course, they are so perfectly interwoven that the first shot must set up the second shot, which must set up the approach. In reality, doing so may make the hole pretty unplayable, and the middle shot ends up pretty bland in the name of fairness. A par 4 is conceptually the strongest hole, which is why more than half of most courses are set up with more than half of them being par 4 holes.
The second is that play spreads out among different levels of players. I recall seeing Muirfield Village no. 6, which featured staggered bunkers up the fw, which was cool, and I thought, never asked Jack or Desmond, that it was to provide some challenge and interest for shorter hitters. It looked great, too as the bunkers marched up the hill. I have always looked for the possibility of a similar par 5, but the few I actually have done, have had all the "excess" bunkers removed for lack of play over the years. So, there is more often the question of whether any particular sand or steep bank grass hazard is "worth it" for a small, almost random level of play it might receive between two par 5 landing zones.
Lastly, there is the "distance" problem. For pros, there aren't any par 5 holes left. But, at the courses I design, who cares at most? Even low handicappers, with 290 yard drive/260 yard 3 wood, a 550 par 5 is the limit of reachable par 5 holes. If we use the old Gary Player mantra of one unreachable, one reachable, and two tweeners, all we need is on at 575+, one at right around 500 (265 yard drive/235 yard second, and also, the minimum under the rules) and two in between, say, 550 yards and 525 yards, and every day players have fun reaching maybe 3 par 5 holes. Not a huge change from 40 years ago for the low handicappers. You might favor slightly longer.
On the short end, 405 is the minimum par 5 for women, but for many, with a 140 yard tee shot, and two 120 yard 3 woods, 380 yards is all they can reach. Similar for senior men at 170-150-150 - they should probably never exceed that 471 minimum for par 5 holes by USGA standards.
I presume the question was aimed at my middle point - can we make the second shot truly interesting strategically. While yes, it seems it happens pretty rarely. If I had time, I could speculate as to why.