That is one ugly-ass bridge. A bridge to the IOW would almost certainly need to be prettier, which would probably make it more expensive.
ETA: I’m not saying we don’t have some equally fugly bridges right here already, but plonking something like that down, right in the middle of a piece of touristy and fairly-picturesque seaside would be massively unpopular.
Nice.
Reminds me of the old (now obsolete) joke:
Q. What’s brown and comes steaming backwards out of Cowes?
A. The Isle of Wight Ferry.
Look, I turned 64 back in November, and you never even sent birthday greetings, to say nothing of the bottle of wine!
A couple years ago I was on IoW during Cowes week, one of the island’s busiest periods. The ferries seemed to cope with no problems, so there’s no great need for a tunnel or bridge.
One more thing… Who would use the bridge? There’s no way to site the mainland end of the bridge that would be convenient to more than a fraction of potential users.
Here’s what the place looks like from space:
Working from West to East:
[ul]
[li]Milford-Yarmouth is the shortest span, but is not very accessible from the mainland side (and the wetland to the northeast of Hurst spit is a protected SSSI)[/li]
[li]The coast between Lymington and Fawley is not especially accessible[/li]
[li]There is good road access down to Fawley from the M27 motorway, so a Lepe-Cowes bridge would serve tourists, but this (and all of the above) would be useless to commuters to/from Southampton, Gosport and Portsmouth[/li]
[li]Gosport-Ryde is impractical - road access in and out of Gosport is a perennial and hopeless problem (to the extent that property prices are low in Gosport because it’s a nice place, but you can’t get in or out)[/li]
[li]Portsmouth-Ryde would be useful to commuters to-from Portsmouth, but useless to everyone else, including tourists, because Portsmouth itself is an island with only one good road link to the mainland (and this road only gets you halfway down before it turns into a traffic nightmare.[/li]
[li]Hayling is too far to the east, and a bridge from here would be useless to everyone except tourists, and then only with major development of a link to the A27[/li][/ul]
Basically, it’s hard to get from any bit of the solent shore to any other bit, and it’s not especially easy to get to the solent shore from the motorway.
So if they built golf courses along the shores, would the landscaped parts be Solent Greens?
I was pondering that myself the other day - I’m quite surprised there isn’t a ‘Solent Green Business Park’ or some such, but there doesn’t seem to be.
We could build a bridge to the Isle of Wight if it’s not too dear. We could scrimp and save.
Roundabout
From what I know about British politics, I shudder to think what would happen to a government that actually tried to build such a bridge.
The population of the Isle of Wight is made of people!
Well, almost.
Spent a week on holiday in Ventnor on the Isle of Wight in 1989. The ferry was very efficient and part of the fun for my children.
Which probably means the cost for a somewhat shorter bridge built 20 years later would indeed be multiple (in the sense of at least two) billions of dollars.
If it’s anything like the Spinnaker Tower project, they’ll run out of money half way and have to decide to carry on building the bridge, but just make it shorter.
Different song, different group. 
Anyway, there won’t be a bridge to the Isle of Wight, because then it bloody well wouldn’t be a proper island anymore, would it, and they’d have to rename it and rewrite the songs and rename the music festival and harrumph harrumph!