Is chess 960 is useful in developing standard chess?

It is a matter of preference. If you want to play 960 just to improve at standard, then you might as well spend that time playing standard instead. 960 is more likely to give rise to thought provoking positions, but that's all there is to it, 960 is still chess, the ideas are still pretty much the same. Both variants count as experience, if you play 960 more often, you will still improve at some aspects and miss on at the others, & vice versa.
However, if you feel uncomfortable going into the uncharted, or have problems understanding pawn structures, 960 can be pretty useful. It often gives rise to closed positions where the importance of pawn structure is emphasized -at least what my experience suggests-, and for the uncharted part, well that's kinda the point of 960.
There are other variants of chess that focus on other aspects of the game, thus might improve your understanding.
-Three check: Check the opponent 3 times to win. Checkmate also counts. Piece development, attacking the king, gaining tempo, forcing sequences, defense.
-King of the hill: King to the center of the board wins. Checkmate also counts. Controlling the center, piece development, defense.
-Antichess: Losing all pieces/getting stalemated wins. King is an ordinary piece/can be promoted to. Captures are forced. Deflection, forcing sequences, weaknesses/strengths of the pieces.
-Horde: 32 pawns v. the standard piece set. Black wins by taking all pawns, white wins by checkmating. Creating counterplay.
All the above are available on lichess.org
TL; DR: From an objective standpoint, 960 will help you just as much as standard chess overall, but it may help you with different aspects of the game you otherwise don't show improvement on.

Levon Aronian, a world champion in Chess960, argued that the better the player, the less difference it will make whether it's chess960 or chess. The principles are still the same.
He pointed out that there are too many "ridiculous" starting positions in chess960, and has pretty much given up on the variant.
I tried chess960 a few times, but I'm sticking with classical chess.
YMMV.
2023 update: Aronian has recently said that he loves 960. There has been some talk of eliminating the positions that give White a large advantage from move one. There have been enough games for a database of every legal starting position. Some positions are nearly equal, some give White a large edge.

I've improved a lot in standard since I also play 960. Against the standard opinion, it's strategical thinking that has developed further. Middle and end games rules are exactly the same. Structures are new to both players, so pattern recognition doesn't make a difference

a pretty studious guy I know feels that chess960 strengthens regular chess. it's thought provoking, and you have to think of a lot of concepts that in regular chess are possibly 'automatic.' I feel it might help, but in general it provides many (er, I mean 99%) positions that are unheard of in regular chess. so, in a word, useless for regular chess improvement.
I don't see how chess960 could help regular chess much ---- more, it would hurt it. why not play any of the other variants, extra squares or extra pieces, or whatever? to me, all these variants, 95% of the time, they'll hurt your regular chess much, much more than help it. I think chess960 is ok for fun (altho not for me lol), but is a poor tool to improve regular chess. the patterns of regular chess simply don't exist in chess960, and so you are not building that recognition.
I can see how chess 960 might help the end game, but that's only because then most of the chess 960 'nonsense' has been played out. so, actually, it's not helping your end game, imho. it's just pretty similar to regular chess, at that point.
Anyone care to take up the gauntlet for chess960?
Is it useful or useless?