The difficulty is you have to achieve traction and scale to compete with a company that's making tons of money exploitatively and user-hostilely strip-mining their own system and running on low margins with high reinvestment due to their scale and (stock market) reputation. Good luck.
See also: voice interfaces. Your nifty paid version that's entirely local? Good luck competing against free, cloudy, and data-stealing, especially when the data-stealing helps the competing services get better. There's a reason local voice-to-text seemed to be getting really good for a while then suddenly dropped into obscurity.
See also also: any paid (or even free and volunteer-based!) website or service that might compete with ad-paid and/or information-harvesting and free. Uphill battle to gain user-share. You'll almost certainly fail, because information-harvesting is a possible business model and no matter how much people hate it they can't organize to stop it, realistically, because game theory (ahem, which is we have governments, in the short-short version)
I see it on here from time to time on here but have never heard a person in real life mention it, so... maybe?
Incidentally, I'd pick map & navigation data as the one big Web thing that really ought to be handled by government. Up-to-date, freely (or very cheaply) available map data should be considered infrastructure, and government(s) ought to already be generating/collecting it. Let the private market get it to consumers, but governments ought to be providing good-enough data that there's no need for private collection of it, in the general case. Leave street view and business reviews and such to Google and friends, but enough data to build a pretty damn good navigation app should just exist for anyone to use. It's a huge waste of effort to have multiple organizations trying to put all that together and it's something governments should to already have the data to provide, given some coordination—great candidate for a government service, or at least one of those government-coordinated public-private shared-cost-shared-benefit projects, post-war Japan style.
See also: voice interfaces. Your nifty paid version that's entirely local? Good luck competing against free, cloudy, and data-stealing, especially when the data-stealing helps the competing services get better. There's a reason local voice-to-text seemed to be getting really good for a while then suddenly dropped into obscurity.
See also also: any paid (or even free and volunteer-based!) website or service that might compete with ad-paid and/or information-harvesting and free. Uphill battle to gain user-share. You'll almost certainly fail, because information-harvesting is a possible business model and no matter how much people hate it they can't organize to stop it, realistically, because game theory (ahem, which is we have governments, in the short-short version)