It isn't needed yes, but the Eldin Bridge Warp point is fairly close to the Hidden Village, which is where you get stuff that I've long forgotten ever since that trade sequence was skipped. The nearest warp I can think of other than that would be the one next to Iza's. Eldin Bridge warp is probably slower though since that one requires 3 warps vs 1 warp to Iza's
58s faster to warp the bridge piece.
WITHOUT BRIDGE
-Gerudo Desert cannon landing to camp = 53s
-HC warp, wolf to HV = 2:17
-HC warp, Epona to Sky Book Statue = 2:18
53s+2:17 = 5:28
WITH BRIDGE
-Gerudo Desert cannon landing to Shadow Beast fight + bridge warp and back to camp = 3:00
-Eldin warp, wolf to HV = 1:00 (probably a bit faster with Epona)
-Eldin warp, wolf to Sky Book Statue = 30s
1min+3min+30s = 4:30
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5:28 VS 4:30 = 58s faster w/ bridge
No need to visit Iza at all so that warp location isn't unlocked in the first place
EDIT: Oh there's a sky book page right by Mesa too, so that would save maybe a minute too