There is a question in the title of your post. The answer is yes.
Now, for the rest of your questions, I want you to visualize being disappointed with virtually all of the actual measurable sail to power comparisons you have laid out, plus others. Almost all of your concerns are based on speed, range and transport utility.
You have already quantified the only one of those metrics that will improve (MPG), with the possible exception of heavy storm seaworthiness. You're question about being able to use your motor during a storm (you can) is cool to me because as a life long sailor I always have wondered how power boaters have the guts to depend on just one motor while boating in dangerous weather. Very different outlooks, but not in a bad way, just what we've learned by experiences.
If you can imagine having to check ALL your speed and transport efficiency expectations at the dock, only then will you have a chance at sailboat satisfaction in my opinion.
Get the sailboat, but you've got to treat it more like snow skiing vs water skiing - they are that much different.
Here's some minor pleasures I enjoy from having been a life long sailor.
Less danger from self inflicted collisions and equipment failure requiring a tow- my parents shared the skippering responsibilities with us kids, took longer adventures and later trusted me and my brothers and sister with the boat ourselves much more readily than one with a lot of horses. My kids are old enough to take out the boat now, even if they just go for a short daysail, they love the independence and as you said there's no gas bills so the extra use while I'm not on it doesn't cost any extra.
The total absence of engine noise while sailing. It's great for relaxing, listening to music, eating , having cocktails all while slowly cruising either to a destination or just messing about.
The ability to have a blast on days when the swells seem to make most of the under 30 foot power boats stay at the docks or on their trailers.
The extra element of complexity and skill required to sail. Don't take this as snobbishness, most anyone who put's their mind to it can master competent cruising. I mean it in the same way that mountain climbers, cross country skiers, and snow shoers etc. find the challenges of their sports personally exhilarating and less boring than walking or jogging.
I could go on forever just as you probably find lots of stuff unique to powerboating quite rewarding, and the things I list above probably seem like they only have subtle improvement potential over your experience on your powerboat and you might even see some as detriments.
Don't go completely cold turkey on the joys of motorboating either. Budget for and buy a nice inflatable dingy with a good sized reliable outboard for your dink. If your family likes being towed behind your boat on various things, keep the ones that can be towed behind your sailboat and inflatable. I don't have the dough but one of my friends has a big sailboat AND a fast little no cabin runabout for his occasional need for speed.
I personally love being invited out for some speed boating, it's a blast, but it's interesting that motors have only been on personal boats for the last 70 or 80 years or so. When wondering whether you'll get enjoyment from sailing vs. motorboating, imagine you were born in one of the thousands of other years before that, do you think you and your family would have left the oceans and lakes to us sailors, or do think you might have seen the attraction and had some fun? I try to spend less time deciding what I do and don't like and look for the laughs and thrills in everything.
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