I'm sure companies wouldn't mind if a singular person was doing singular things with the API, but when someone uses this API to behave like more than 1 person is where companies get annoyed.
To use an annoying analogy or two, take a penny leave a penny but someone shoves their hand in there and takes all of it.
It costs money to service requests and twitter et all make that money back through advertising and subscriptions. If someone uses an unauthorized API, it could use more than they've budgeted for.
Actually they'd also get annoyed if everyone just used something like this for themselves. They want to control your experience. And as usual, remember you are not the customer, you are the product.
To use an annoying analogy or two, take a penny leave a penny but someone shoves their hand in there and takes all of it.
It costs money to service requests and twitter et all make that money back through advertising and subscriptions. If someone uses an unauthorized API, it could use more than they've budgeted for.