Then you are a uninvited bot that crawls my content in order to send alarms to people to tell them to visit my site?

This is a "what if it's for your own good?" argument. What if I break into your house to clean your toilets? Although amusingly, if you're a "web alerts company" that I didn't contract and sends out alerts in batches on your own schedule, you will probably send a ton of your customers to my site at the same time and slashdot me off of the web entirely.

No, I won't send a ton, I'll send a few dozens to a few hundreds at most because not everyone is interested in the same things. And they'll visit at their own timeline. If your site can't service a few dozen requests simultaneously then you probably aren't a news site in the first place so the whole argument is moot.