I realize that not many people were fond of LP3, specially given its radical departure from the gameplay mechanics that started with LP and which were further refined for LP2.

Personally I think LP3 should have been rather classified as LP0 or LP Origins, which would have emphasized the fact that the game was not meant to build upon what we saw in LP2. I also think they should have exclude the multiplayer mode since it really doesn't fit with the game, specially considering that there are no actual VS in the main story, which in turn resulted in a single type of VS for the multiplayer mode. I thinkt hey should ahve made two separate games: a single player game and a multiplayer only-game, which would prevent either from being limited to the setting, gameplay mechanics and weapons available on each one.

Seeing how Capcom is now pushing for a multiplayer only RE game, Umbrella Corps, I think they could also take a similar approach for LP. Personally I think it has more potential for a multiplayer only game which picks up from the gameplay that was developed for LP2. Furthermore, a multiplayer only shooter would be more fitting for LP given the action-focus of the series, unlike RE which is more about its survival horror theme.

Any thoughts about this?

What would you like to see in such game?

I honestly think Capcom should have made a Lost Planet shooter their big announcement instead of Resident Evil Umbrella Corps, both series have sold millions but only one was a shooter first with a massive scale in movement and action to boot. Now that they are working on Umbrella Corps though, yep, I'll did like to see a Lost Planet N.E.V.E.C. Corps or whatever, especially if it let play as the Akrid or interact with them a great deal during normal battles.

I have Lost Planet 3, but haven't started playing yet, given what I've heard about it and how it has another development team which aren't even around now, it definitely would have been better to frame it as an origin story through something like "Lost Planet 0" or "Lost Planet Origins". Both of them still imply more shared mechanics than it did have especially since some "Origins" and "Zero" titles have more mechanics like Yakuza Zero or Resident Evil Zero, but yeah.

I didn't play much of LP1 (none but a demo years ago) or LP2 (coop for a bit, competitive for a bit) multiplayer, but E.X. Troopers seemed to have a good model to work off. I'd like to see a game take both the jetpack for quick movement along with the grappling mechanic to make something a little more fast paced. Of course, I'd like more weapons and lots of V.S. even if I think E.X. Troopers made weapons more interesting through how the elements worked and balanced out. 

Depends on how they balance it. The jetpack which popped up late into Lost Planet 2's story let you air dash around and past considerable parts of the stage even if it was a very open few missions in space. E.X. Troopers basically has it in the place of dashing and the disadvantages are that you have less turning options, notable lag on ending the dash (which has a limit) and only few techniques which can be done from it (Jet Melee, Jet Primary Weapon and Jet Secondary Weapon not all secondary weapons work as well).

I do like the real time weapon and equipment changing in Lost Planet a great deal, but if everyone had a E.X. Troopers jet pack and Lost Planet anchor to start with (or picked between the two!), it would be pretty interesting even if rebalancing may be needed.

Elemental weapons wouldn't even be that new given that there are already flame and paralysis weapon types whether it is a gun or a grenade, my point is that even without messing the health system so people have to pick their favourite armour, you could have more interesting battles if these properties played more of a part by being part of some other weapons. It doesn't need to apply to all weapons, it doesn't even do that in E.X. Troopers (it equals more damage on some Akrid types - has an effect only in specific attacks) but it works to encourage clever movement in the game since Fire damage can be canceled by dashing (not jetting), being frozen can be cancelled by a friend kicking you (much like Monster Hunter) and being paralysed... is basically the same as Lost Planet's grenades.

The hub was a great addition, but I think they will have to return to focusing on a smaller cast of named character for it to work for a main series Lost Planet game. I don't think the LP1 story was poetry, but it was easy to explain in brief "Boy fights pirates and monsters, gets revenge for dead father" (Wayne should have had a hub for part of the story at least). I did have a few groups I got attached to in LP2 (DESERT PIRATES!), but being undefined groups of 4 or bigger where they didn't take the risk to name, harm or kill even the extras wasn't great even if the massive effort to team up to save the E.D.N. III was novel. E.X. Troopers had more going for it than Lost Planet 1 and let us enjoy all of the cast members storywise.

Assuming a new LP game was to have a hub, it would be nice to focus it on something.

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Oh and on the off chance someone who reads this hasn't played E.X. Troopers to know how it compares and contrasts with other LP games... It is actually more like a grounded Gotcha Force or Gundam vs Gundam than a Lost Planet as far as general combat goes:  

You might see a few special attacks and honestly I think they would need to be rebalanced to work in E.X. Troopers competitive multiplayer to begin with. Perhaps with less invincibility frames for using them, quicker activation and some smaller E.X. Thermal attacks using only 1 or 3 stars with no invincibility, not that players can't pick a special which circles around you probably being the best bet for that.