I may be a bit late to the party, but I still thought I would like to add my thoughts on why I like D&D 4E:
1. It (still) feels like the most modern D&D implementation. Since it took inspiration from many other forms of games:
- The clear, precise and consistent wording was clearly taken from Magic the Gathering
- Teamplay was inspired by Football (soccer) thus the names of the 4 roles
- Layout for encounters are clever and on a single double page. Similar to what a lot of modern boardgames (after 4E) do. Like Stuffed Fable and similar games
- Lots of movement and forced movement and dangerous terrain fully embracing the grid like Final Fantasy Tactics and similar games
- Having the same class structure for all classes, to make it easier to learn other classes, like pretty much EVERY modern computer game like Mobas(league of legends), teambased shooters and others do (and later also RPGs like PbtA) as well as a lot of boardgames do.
- Having simplified statblocks with all attacks on them (no looking up spells) like boardgames do
- etc.
2. It improved A LOT over its initial run even though it was only 5 years. Yes not everything was perfect when it released, but wow did it improve and listen to the community ( bit too much even).
- Players did not like that monsters scaled over higher hit chances and defenses, so this was changed via new feats
- Since players felt there was a feat tax for the expertise feat, later expertise feats had a nice bonus for a weapon type
- Players did not like that monsters were now too weak (because of the feats) so Monster Math 3 fixed this problem
- Monsters in general were too defensive, so later monsters (MM3 and later) were in general more offensive designed
- In general monster design improved over time
- The game was released with no simple classes, later with the Essentials simpler classes were introduced-
- The first Essential book was (understandable) critized, and the later books did the simplified classes a lot better and had some really elegant designs.
- Similar (people who were not used to modern game design) did not like that all classes had the same layout and thought this makes them to similar, and from PHB3+and Essentials on several classes with different structures were released.
- The paladin and cleric were lacking cha powers, so the power source books made this better. Paladin also got more ways to protect allies, since he was lacking those
- The game was received as having "only combat", so LOTS of non combat/flavourfull parts were later released (Character Backgrounds, Character themes, Skill powers, martial rituals, more rituals, epic destinies with more non combat fluff, Essential classes with more non combat parts)
- In general lots of errata and fixes to make the game a smoother experience, because they cared so much about balance
- Skill challenges were in DMG 1 unclear and tooo hard (the way people played), so the math was changed and then the DMG2 made lots of examples and made them clearer on how to use.
- The first released adventures really sucked, while there were some gems among the later released adventures. (Greymore abby, Slaying stone, dungeon masters kit and others)
- Later rules were added for GMs/players who would prefer to play with phewer items.
3. It just has a lot of really good content. Of course there is also some filler stuff and some weak feats and powers, but it also has really a lot of great content and not only for classes but also for monsters, magic, traps, settings etc.
- It has 4 well made and quite varied (from each other) settings. (Nentir Vale, Forgotten Realms (Including a fleshed out Neverwinter), Eberon, Dark Sun).
- It has around 40 different classes with different powers. From simple to complex and with different flavours and power sources.
- It has around 40 races all with their own special ability (although feat support was uneven).
- It has 100+ themes
- 100+ epic destinies
- 100s of paragon paths
- Some really flavourfull books like Heroes of the Feywild
- An interesting adventure hub with Hammerfast
- A book with 30+ mini dungeons etc.
- 2 REALLY GOOD DMGs which are better than the 5E DMG even for 5E...
4. It has just really good and elegant math, and well working balance. Pathfinder 2E uses the base math system (just with a factor 2). This together with lots of other features (monster roles, traps/dangerous terrain with xp value etc.) makes it easy for GMs to build encounters:
- Monsters were balanced enough, that its enough to look at their level and their monster role to choose them, you dont have to double check if they are not too strong or weak for their CR
- A "normal" encounter is really easy to build. For ever level X player you add 1 level X normal monster. Done (So easy per player scaling)
- A hard fight would be just 25% more monster and a deadly fight 50% more
- Simple rules to replace monsters. 2 Normal monsters = 1 elite, 5 normal monster = 1 solo, 4 minions = 1 normal monster
- Really simple rules to use higher or lower level enemies: 2 Level X Monster = 1 Level X+4 monster. 3 Level X monster = 2 level X+2 monster. 5 Level X monster = 4 Level X+1 monster
- Traps and Dangerous terrain have XP and can just replace monsters with roughly the same xp value. Also simple rule (on Page 42) to build traps (damage per level etc.)
- Monsters have different roles, to easily know how they play. This makes it easy without much research to make different feeling encounters just by using different level adequate monster types.
- Really simple rules for non combat XP. (A long skill challenge is equal to a same level combat encounter. A normal group quest as well. 4 Personal quests as well)
5. There were just so many good ideas, which inspired many other games, and can still be used as inspiration!
- Skill challenges are still used and also inspired the Clocks of Forged in the Dark
- The hybrid class system is used in 13th age as its multi class system
- The normal "weak" multiclassing is used as the Archetype system in Patfhinder 2
- The base combat math and encounter building (with small tweek/ factor 2) is used in Pathfinder 2E
- The skill powers are used in Pathfinder 2 as skill feats
- The 5E background unique abilities, are quite similar to the later non combat powers of classes (especially the bard)
- The combat system inspired many modern games (and still does) like: Gloomhaven, 13th age, Strike!, Icon, Lancer, Gubat Banwa, Pathfinder 2, the new MCDM RPG etc.
- The epic destinies are great inspiration for endgame goals of players!
- The character themes are great inspirations for backgrounds. And include some really cool mechanics.
- The Essential Ranger and Sorcerer are great examples on how to make simple characters still interesting while being elegant. (I know many people did not like Essentials (most likely because of the first book), but the Scout Ranger is a really elegant "bring down to the essential" version of the multi attack ranger, with great nature flavour, the Hunter Ranger is an interesting archer ranger, which does more than just damage (namely providing support and controlling the battlefield, like Hawk Eye in the avenger movie) and the Elementalist Sorcerer shows that you can make a good simplified caster, something 5E and lots of other games never managed)
- The many unique solo monsters are good inspiration for boss fights, and even though also them did not work perfectly, they are still miles ahead of most other games solo encounters