What a depressingly elitist and exclusionary view. The modern web browser contains all the technology right there to make fast, maximally-accessible websites and even some “app”-like things, but nah you can’t be bothered, screw the less-fortunate. Would you want to “just go to a library” instead of use the device you already have? I strongly doubt it.
Public libraries are great and there should be a lot more of them and everyone should enjoy them, but they should absolutely not be a substitute for respectful, accessible web design and engineering. The elitism is that only people with the shiniest new devices should get to use your website on their terms.