I have a specific email folder for speculative applications, whether it's for jobs of any grade, PhDs, or Masters courses. It's called Spam, and all the speculative job applications go in there.
If I'm feeling exceptionally generous, I reply with a link to the University vacancies page.
And that's because one of the defining elements of academia is rigour. That means, among other things, being able and willing to follow experiment protocols. If the first thing I learn about a potential colleague is that they can't be bothered to follow our recruitment protocols, even though they're well-documented and linked to from our recruitment pages, they've pretty much already disqualified themselves from being an interesting candidate, unless they're really exceptional. (And as we know from Dunning & Kruger, the ones who think they're really exceptional, typically aren't; and the ones who are, typically think they're not.). Those guidelines are derived from legal advice in the jurisdiction of England and Wales. Other employers in the same jurisdiction might interpret the law differently; other jurisdictions will have laws with different implications.
So, as someone sending out speculative applications, at best you spend a lot of time (that could have been better spent researching, publishing, networking at conferences) customising your CV so that it's targeted uniquely at each recipient, taking account of their unique position, and eventually you find a place that has slacker rules, or you find someone willing to break them. At worst, you send the same application to dozens or hundreds of recipients, showing each of them laziness and contempt.
If someone wanted to get on my radar in a positive way, they wouldn't send a speculative application. They'd send me some research they'd done that was likely to be of particular interest to me. They might ask for feedback on an article before submission, or flag it up to me after publication, in a short, concise, email with a link to the article. They might arrange to bump into me at a conference or seminar. They might invite me to work with them on a paper they have in development, that overlapped with some work I'm doing or have done.