Wouldn't the blockchain size become a bottleneck if all payments happened on Bitcoin?
That would indeed create a lot of data. However, there are solutions for this.

First of all, as a normal consumer you don't store the blockchain anyways. Only some nodes like Bitcoin services and generally those who choose to store the blockchain.

Secondly, even as a miner, keeping the UTXO pool available fast is important. They don't need the entire blockchain which shows you all previous payments available at high speeds. They only need to know what unspent money there is and how it's possible to spend it. That's much less. Storing the blockchain itself isn't much of a problem because storage space is super cheep, compared to mining equipment and their energy costs.

And third, what you probably want to know, high activity on the main chain can and very likely will be avoided via lightning networks and payment processors. Both have their own advantages and disadvantages, of course. You can read about lightning networks in the linked Bitcoin wiki article. I wrote about payment processors 2 hours ago in my answer to this question.