I feel that a lot of us are really starting to forget that, really, in the long run, the word "legendaries" are going to lose meaning anyway. For example, think about how many legendaries we'll have in the generations beyond this one. It's not just a problem lying within however many legendaries Gamefreak decides to introduce in this generation, it's a problem with the main series games themselves. I can figure that it'll be around Gen VIII where everyone would be just tired and annoyed of hearing the word "legendary" when the word doesn't even hold true anymore, and instead some other word might replace it.
Something like "Extraordinary Pokemon". That's a lame example, I know, but if GF continues to use legendary Pokemon, then I won't blame them for it, really, but I feel it'll get redundant in the long-run, when a much more fitting term can be used.
Gamefreak itself has different classifications usually. The 600+Base Legends are usually called Phantom or Mythic Pokemon. Most of those have stories and backgrounds to go with their legendary status.
Though I disagree with the "tiring of the term". There are Hundreds of thousands of myths in our world. Do they have little to no meaning because there are so many? No not really. Majority of the Legendary Pokemon are known that way for aesthetic reasons.
Mew, Celebi, Shaymin, Manaphy, Victini, Jiranchi, Meloetta....these Pokemon are just so few in existence or haven't been seen that often except in huge gapes of time.
Ho-oh and Lugia have major legend factor in Johto as they were worshiped.
The beasts are legendary for their astounding speed and ability to hide from capture, not to mention that they were supposedly revived by Ho-oh after dying in a fire.
The Golems and Regigigas, these have a history that spans across 2 regions. Sinnoh and Hoenn. Represenations of the ages and holders of untold power.
Cresselia and Darkrai are fairly well known legends in Sinnoh. Darkrai who causes people and Pokemon to fall into nightmares that they cannot wake from and Cresselia who can cure these nightmares.
Kyogre, Groudon, and Rayquaza have a huge history in Hoenn. Not to mention their power itself is things from legends.
Arceus, well there isn't really much need to touch him. His legend is written all across Sinnoh and Johto (HG/SS add on). By extension Palkia, Dialga, and Giratina's powers are easily vouched for. Despite not using them in actual battle, they all tear rifts in the dimension and using two you could practically destroy the world.
Again through extension, Azelf, Uxie, and Mesprit's legend and powers fend for themselves. They have the power to suppress the three larger legends.
Zekrom and Reshiram's legend shaped an entire nation/region. Kyurem's legend bred fear and a new lifestyle. His legend is later expanded upon which kinda just created holes in the original legend.
The Musketdeers are renown fighters and defenders of Pokemon. Not to mention highly elusive.
The Kami Trio cause storms and create fertile fields. While they aren't huge legends, they still have a good impact. Arguably more than others.
This pretty much just leaves Heatran, the Birds, the Eon twins, Genesect, Deoxys, and Mewtwo I believe.
I can't really say much about Heatran, Birds, and twins. They are Legendary because of how elusive and hard to find they are. Like with the "mirage" legends, they are seen periodically through time in large gaps.
Mewtwo and Deoxys however are most known for their power. Mewtwo a clone of Mew and much stronger than the original is currently viewed as the strongest fighter in existence. Usually referred to as the Ultimate Battling Machine. Deoxys' power rivaled that of Rayquaza, able to go toe to toe and hold his own fairly well against the dragon. He can change form for better fighting capabilities and is just an enigma. Genesect...well his is less impressive. He was a super ancient Pokemon, possibly older than most fossil Pokemon, that was found and remodeled by team plasma. Like Mewtwo he was created to be an ultimate fighting machine.
Legends vary in weight even in the real world. Lesser legends typically become Fairy-tales while major ones stay myths or legends. Number really doesn't kill the meaning of the word so long as there is prominent backstory to go with them. Biggest issue with # of legends is that most have varying battle capability which is pretty much all fans base how good a Pokemon is on now. Type, Stats, Ability, Move Pool. That's what everyone looks at and Legends while slightly better in most of these fields, the combination is never really that amazing. Which is where a lot of disgruntled feelings towards legends comes in.