The worst idea is to buy mana from Vladimir or Riven, because they don't use it. Like it if you laughed too! Gaaaaa!
Now that the rotten joke has been preshot, it's obvious that stats have been factored in against which champions they're useful to . Clearly you can buy a Rabaddon on Vayne, but other than making yourself a nice hat, it won't do much good. The point of view covered will be that of optimization, according to the current meta (December 2022, so the information given here may no longer be relevant after a few patches). Yes all champions use auto-attacks, so technically everyone can do something with AD and AS, but it's clearly not for everyone. And right now, the worst stat in the game is also a stat that one would think is pretty universally ok: HP .
Evolution of the role of VPs over the years
Aside from a few characters who also used the stat offensively (Vladimir leading the way), HP has always been a more tank-friendly stat in most metas. Sure, there were a few exceptions (big brothers remember the Atmog build), but overall HP = harder champion to kill. However, to prevent tanks and other resistant characters from becoming too passive , Riot Games thought of integrating objects and modifying certain champions, so that their damage depends on their PV . This is how the Titanic Hydra first appeared, and how champions like Dr. Mundo and Cho Gath saw some of their spells get an offensive ratio to their total HP . It's not the only defensive mechanic to have undergone this treatment, for example Malphite's W gained a ratio on his armor in season 5 (on the other hand E always had a ratio on armor).
Going back to HP, their original purpose was to make a champion harder to kill, and also to counter characters that dealt raw damage . However, over time, this stat, which was initially supposed to be very clearly oriented towards defense, gradually became a more hybrid stat . What is meant by this is that at the beginning it was a 90% defensive stat and that through the evolutions of the game, it only became a 70% defensive stat. . (values taken at random, it's just to illustrate the point in order to avoid people thinking that we write that HP has become an offensive stat, which is not the case. The stat remains mainly defensive and will probably always remain so) To avoid stupid builds based only on HP , and which not only make a champion very difficult to kill, could allow him to do more than decent damage, other objects and mechanics have been introduced into the game . This is where the problems start.
Current issues
Today, there are many, many items that deal damage based on a champion's max HP . Although the principle is not necessarily recent (the Bloody Razor of Madred present from the start of the game was the ancestor of the BotRK with a similar passive), objects with damage based on max HP have become more and more currents. Early in the game, they only became good in specific situations , and were often shunned by players. Part of the problem came from their effectiveness, because if they were very useful to counter tanks, they were much less effective on DPS. Riot Games has made sure to make them more interesting, to the point that even today against a very fragile composition, some champions will still do the BotRK or the Divine Slayer.
Additionally, champions have started to have raw damage percentage on max HP . The most famous examples currently are Fiora, Vayne and K´Sante . Others have non-raw damage as a percentage of total life, either with magic damage (Gwen, Kog'Maw etc) or physical damage (Jarvan, Xin Zhao, etc) . The icing on the cake, season 13 brings a new tank item, which also does damage based on the max HP of the targets: the Jak'Sho .
All of this contributes HP to one of the least profitable stats in League of Legends. Let's be clear, it is not necessarily horrible or that it should be neglected, but it is often much less effective than others. To resist in a fight, tanks and bruisers will now favor regeneration (except for certain champions who have damage based on their max HP) and even on rather DPS items, HP is not very popular. For example the RoA (Staff of Ages) was an excellent item a few seasons ago, but since its return in season 13, it is rarely an interesting item to build for most mages (with of course a few exceptions). Certainly the RoA is not bad only because of the HP, but it is one of the causes of its weakness.