Ok, name changed for this obviously...
So I live in Cowes and my DC go to Gurnard and I really don't recognise some of the criticisms of the island here! I didn't grow up here and moved here from London too.
Not enough supermarkets? That's just odd. I can drive to M&S, an Aldi, Sainsbury's local and a Co-Op (open late on Sundays) in 3 minutes, a big Sainsbury's, Lidl, Morrisons, Asda in 15-20 mins. There's Waitrose in East Cowes (which does excellent delivery) and a big Tescos in Ryde 40-45 mins away (Also delivers). How many more do you need?!
There's also amazing local food - veg box schemes and fishmongers and farm shops and proper local butchers. There are several great delis in Cowes alone that sell higher quality meals than you'll get in a place like Cook in London, and all kinds of local and imported cheeses... and there are lots of brilliant restaurants. Avoid the tourist tea rooms and you'll eat better here than almost anywhere in the country.
Nothing to do? Utter rubbish. For families with primary age DC there is more than you can fit in on any given weekend of holiday. We have season tickets to loads of attractions - Tapnell Farm Park (best farm park in the UK) and Robin Hill and English Heritage (several locations on the island) and there are plenty more. Between all the special days they put on, and the regular attractions, and annual events, and the beach days and cycling days and sports clubs and all the rest of it we have realised that we basically don't need a garden because we are never in at home. There is ALWAYS something to do as a family.
I appreciate that this may change for teenagers, but the teens I do know have an amazing life - they have more freedom than those I know on the mainland, many do a lot of sport. They also know that while some pubs may let a few well behaved underage drinkers in, if they overstep the mark their parents will hear about it in a heart beat!
For adults, no we don't have loads of theatres and night clubs. But thinking through the friends I know they sing in choirs, go to yoga, Crossfit, are members of several road and mountain bike cycling groups, women's running groups, competitive running groups, triathlon, stitch'n'bitch, sketch'n'wine (not it's actual name!), every watersport you can think of (women's learn to surf classes, windsurfing, sailing of every shape, SUP), book clubs, freelancer meetups...
Then there are the annual events - a Literary Festival, Isle of Wight Festival (I've seen some of the biggest bands in the world then cycled 20 mins home to my own bed), boutique festivals like RhythmTree, lots of sailing regattas besides Cowes Week, which also has fireworks and family theatre shows and everything else.
And most of all just hanging out with friends. It is such a friendly, community-focussed place. I have made more friends here than at any other point in my adult life and I am NOT naturally gregarious.
I have plenty of friends whose parents have moved down here to 'see the grand children' and also found themselves so busy with friends and groups that they are no longer free to babysit the grandchildren! 
There are areas of the island that are totally focussed on the tourism side of things and dead the rest of the year, but it's certainly not all. I have good friends in Cowes, Yarmouth/West Wight and Ryde/Seaview. All are successful, motivated people who have interesting careers and have figured out a way of continuing them while working on the island (transferring to somewhere like Ellen MacArthur Foundation or many of the engineering firms based her, working remotely, commuting occasionally, splitting their week etc). This trickles down to the schools and certainly schools like Gurnard are full of engaged parents who are ambitious for their children.
I fully expect my children to leave home for university and then to start their working life, as did I. But I'd like to think they have enough amazing memories of their childhood here to consider coming back when they have their own families.
Everybody i know here does SOMETHING they are passionate about, that isn't just climbing the career ladder and sending their kids on the same round of ballet/cello/kumon classes.
There ARE problems with health and education but they are not the fault of the islanders, more the lack of representation it has off the island.
We have had excellent care at St Mary's (paediatrics, maternity, NICU etc) and many specialists from Southampton or Portsmouth have a rotation day on the island so some appointments can be made here. Yes, some treatments you will have to go to the mainland for, but again unless you live in a big city you are likely to have to travel for specialist care anywhere. there have been some very negative reports made about care at ST Mary's but I'm quite cynical about them, it's well known that the Tory NHS policy does not allow for local hospitals to offer disproportionately expensive high quality specialist care, and they'd like to close St Mary's and have us all go to the mainland for treatment. Again, running down of good local NHS services is not limited to the IOW. I am praying that the fact we have so many retirees on the island will mean it is always economic/politically expedient to maintain having a hospital here.
Primary schools are mixed but rarely oversubscribed so you can find the one that suits you best.
Secondary schooling is a problem. We are budgeting for private and we're not the only ones. Other families have chosen the Free School on the south of the island which is supposed to be excellent, and I am hearing increasingly good things about Cowes Enterprise College. Others go to Brockenhurst in the New Forest for 6th form which by all accounts is a great stepping stone to university style learning.
Ferries are expensive, especially at peak prices, although many people are able to secure resident's/discounted rates through their employer.
The very few day to day things I miss on the island are good oriental food (Thai, sushi, Goan...), a better choice of independent cinema, and a better choice of good hairdressers.
I would not consider commuting to the island. You would be paying mainland property prices, ferry commuting costs, and have none of the benefits of living here. You could rent first to try it.
I would also definitely recommend living on the north side of the island with good transport links (mainly Cowes area or Ryde area) to start with. When we retire we'll probably go West! (in 40 years...).