How do you inagine "giving you bitcoins" will work without you doing something equivalent to sending bills or charging credit cards?

Sure, you can publish your wallet address and tell them to send you money. How do you give them access to your content after they have sent their money? How is Bitcoin helping compared to you publishing your IBAN account number and asking for money to be sent directly there?

I'm not very far on my project at all but I assume that a public ledger could tell me that somebody transferred money to the wallet associated with my application.

I wouldn't need to "send bills" because I wouldn't know who my users are. Except that when they login with their crypto-id my application will do work for them, because they have crypto-paid for it.

I wouldn't need to charge credit-cards since they transfer the bitcoins to my account. I only need to know their id and that they have paid me a specific amount of crypto, and that id has used a certain amount of my application.

There needs to be the infra-structure associated with crypto-currency, but not much else. That would make things simpler, I assume. That's my point. Crypto can presumably make payments and user-accounts management simpler. The less you know about your users, the less there is to manage.

Yes, but how is this different from charging a credit-card or publishing an IBAN?

The webshop exposes some way of receiving value tokens, be that USD, EUR or BTC, and has some way to tell which user transferred how many tokens.

So technically there is no difference.

The difference is, I can be pretty sure that EUR won't lose 20% of their value overnight.

If you want to take a credit card, you need to open a bank account, sign up with a payment processor and integrate with them (stripe makes this easy, what if you can’t or don’t want to use stripe?), handle chargebacks, etc.

If you want to accept bitcoin, you run a piece of software and write a few lines of code.

Yes, and for these extra steps the money I earn is realistically not in danger of losing 20% of value overnight, can't be lost because the harddrive that held my password-safe got corrupted, the transactions are done instantaneously instead of whenever some miner feels like including them in his block, and the amount of energy required to process the payment, is probably not much more than I currently use to write and send this post.

I am okay with that.

Yep. Want to accept onchain bitcoin? When a customer wants to pay, generate a fresh address. Store that address in a dab associated with the customer id. When they come for the service, see if that address has received payment. Easy peasy. You can run your own node and do this all yourself, or you can use services that run the software for you and work on callbacks or api calls.

Want to accept lightning (bitcoin over a low cost and high speed payment network)? It’s an api call to generate an invoice and another api call to see if that invoice has been paid. Again you can run everything yourself or use a managed service. Bitcoin make programmatic payment processing SO MUCH EASIER than traditional payment rails.

How would you deal with things like VAT?

This. Building a webshop with crypto is the most trivial thing. Complying with all the legal regulation that buyer and seller are bound to is the actual complex part. Insanely complex.

this is the whole point of Ethereum and smart contracts.