There is never going to be a definitive answer to this question. However, after looking more closely at the list of removed moves, I think I can identify a few trends that might indicate some of the developers' intentions for clearing out the movedex. There are many gaps in the logic, though.
In short, each move seems to have been removed because it fits a particular 'category' of some kind that the developers no longer want in the game. I'll list them out below, and explain each with some examples. In order of confidence:
The move was exclusively a Z-Move: Z-Moves and their Z-Crystals were retired in Sword and Shield.
The move was introduced for Pokemon LGP/E: Pika Papow, Veevee Volley, and the various type-inspired attacks learned by Partner Pikachu/Eevee were all removed for Sword and Shield. It's clear they were designed only to accompany LGP/E.
The move was an unpopular signature move for a Pokemon: Moves like Bone Club, Heal Order, Kinesis, Smelling Salts and Barrage were signature moves that went unused on Pokemon that were already quite unpopular. Heal Order is somewhat of an exception, and you have to ask why moves like Present on Delibird remain if these other ones do not.
The move brought about a unique game mechanic: Many of the removed moves were one-of-a-kind, in the sense they had a unique function that was shared by no other move in the game. An exhaustive list of them should illustrate what I mean: Assist, Bide, Embargo, Flame Burst, Frustration, Heal Block, Hidden Power, Ion Deluge, Magnitude, Me First, Mirror Move, Natural Gift, Nightmare, Psywave, Punishment, Pursuit, Rage, Refresh, Return, Rototiller, Secret Power, Sky Drop, Snatch, Synchronoise, Trump Card, Wake-Up Slap and Wring Out. Of course, there are many other moves that are unique but remain in Sword and Shield. With a few exceptions, this batch of removed moves contains none that were of consequence in competitive play or that were popular with fans, which could be a discriminating factor.
The move was particular to a distinctive and small group of Pokemon: This explanation comes with the caveat that there are many moves that fit its description that remained in Sword and Shield, and also the problem that its boundaries are very loosely defined. However, moves like Heart Stamp, Ice Ball, Clamp, Magnet Bomb, Karate Chop, Camouflage, Rolling Kick, Steamroller, Dizzy Punch, Spider Web, Miracle Eye, Chip Away, Sky Uppercut, Constrict, Sharpen, Bestow, Needle Arm, Spotlight, Meditate, Egg Bomb, Odor Sleuth, Captivate, Spike Cannon, Lucky Chant, Twinneedle and possibly others were only learned by Pokemon with very particular features (e.g. Heart Stamp for 'love-themed' Pokemon, or Odor Sleuth for canine Pokemon) and were thus extremely niche. Many of these moves were also unpopular competitively.
The move was outclassed: This explanation could help categorise moves like Feint Attack, Bubble, Mud Bomb, Jump Kick, Signal Beam and Mirror Shot that I can't explain otherwise.
The move raised all the user's stats: Ominous Wind and Silver Wind are similar moves that both got the boot. Strangely, Ancient Power remains in the game, so this could be mere coincidence.
The move dealt a set amount of damage: Sonic Boom and Dragon Rage were both removed from the game.
The move had a 'type-suppression' effect: Mud Sport and Water Sport were both removed from the game.
The move was an old and now-irrelevant HM: Flash and Rock Climb can fit this category, though plenty of other former HMs like Cut, Rock Smash, Strength, Whirlpool and Dive survived the culling.
Oddities: Foresight, Comet Punch, Barrier, Grass Whistle, Razor Wind and Double Slap are moves I had trouble fitting into any of the above categories, or fitting into their own categories without sounding arbitrary. It's likely there's something about them I simply haven't considered, which you're welcome to comment about.
In summary, I think the developers have removed moves they perceived to be unpopular and restricted to just a few Pokemon, or that introduced game mechanics they no longer wanted for unknown reasons. Despite the removal of Pursuit, Return and Hidden Power, I think some care was taken not to interrupt the competitive game with these changes, considering some of the omissions from the list and how bad most of these moves were.
In case you were curious, Switch cartridges hold 32 GB of memory, and Sword and Shield are only 9.5 GB in size, so the moves were not removed to save space. I highly doubt removing moves would be the developers' first solution in the event they did make a game that was too large, anyway.
The argument that there were 'technical problems' which led to the removal of moves is plain speculation, and unlikely for a major studio game released in 2019. Game balance is even harder to argue considering that 95% of the removed moves are utterly irrelevant in competitive play (and also that the developers have made logical game balance decisions in the past).
EDIT: Here's an interesting take from PokeaimMD on why Pursuit was removed from the game, and more broadly, on the developers' habits balancing Pokemon over the years. He makes a good point that many of their changes in the past have been reactions to the meta that forms in official VGC Worlds tournaments.
