That is true - but it is a common grievance against 4e (HP inflation).
That's not unusual, there were a lot of common grievances against 4e that were not based on the facts of the game, itself, but on, at best, faulty perceptions. 4e changed the way CON affected hps, which resulted in characters having more hps at 1st level, and gaining hps more slowly after that. A 3e character at higher levels could easily have double the hps of a 4e character, a 5e one could get pretty close to that, too.
Personally I enjoyed the gmae - but then again I was never wedded to D&D as some awesome system. It was always a hodge-podge of concepts thrown together - 4e actually bought a unifying design mechanism to the game for the first time - albeit not to many people's tastes.
D&D stayed the #1 RPG until Essentials, and later surveys showed that the majority of D&D fans are fans of the game in general, not hung up on editions (or so I've been told, I haven't seen those surveys). There was a small minority of the fanbase who vocally hated 4e, and a small minority that vocally defended it - a lot of sound & fury known as the edition war. Unfortunately misconceptions spawned by it continue to contaminate discussions to this day.
5e is interesting in that the proficiency bonus is strictly bounded between 2 and 6, so inflation is curtailed. I have some hope that (outside of magic) the game may be playable for much higher levels than previous versions.
It's always been a chicken-and-egg question whether D&D campaigns tended not to go much past 10th level in the past because that was all people were interested in playing, and therefor testing and development of the game at higher level was sparse, or whether inadequate development effort devoted to the higher levels resulted in the game being less playable, and that's why campaigns didn't go into the higher levels often. Either way, there were two large factors in making high-level D&D less inviting.
The first is simple math. It seems pretty obvious that, with 3e and earlier editions, there were numeric disparities among characters that went from barely-differentiating at low level to problematic at high level. BAB, saves, and in 3e, skill ranks. In 3e attack bonuses within a high level party could vary by 5 or 10 or more quite easily, and the gap between the highest and lowest check in a given skill might easily be 30+ - challenges that barely tested one member of the party might be completely impossible for others. 4e and 5e both solved that problem by putting everyone on the same progression. The 4e progression was +15 over 30 levels, while the 5e is +4 over 20 levels. What bounded accuracy accomplishes is to make very high level characters only a little better at most tasks than low level characters. In theory, that makes large level disparities viable within a party (though, AFAIK, that's not the point).
The other is the power of higher-level class abilities. At some point, the number, variety, and power of spells would just become too much. Again, it was most obvious in 3.x at high level, with 'Tier 1' prepped casters, 'god-Wizards' and 'CoDzillas,' but the cracks could show as early as wizards acquiring Haste at 5th level (and practical use of Quicken Spell at 9th), or Polymorph at 7th. E6 play was one solution. 4e removed the problematic spells completely, or 'nerfed' them into very limited rituals (Teleport, for instance), and put all classes on the same AEDU schedule, so it was playable and reasonably balanced through all 30 levels. 5e returns to 3.x and earlier style spell progressions, but reigns in some of the most notorious spells, and limits a few of them with concentration, even as it makes casters more flexible than ever, and casting in combat safer than ever.
My point was that HP inflation did not begin with 5e - far from it. The version where characters could expect the highest inflation was 3.x.
Which is true, certainly. 2e & earlier and 4e had curbs on hp inflation at high levels, while 5e returned to the 3.5 system, but with a stat cap of 20.