How to handle irrelevant employers we don't really want as separate contacts?
One of the distinct advantages of CiviCRM is that nobody is limiting your number of contacts.  Although there is admittedly a bit of overhead in maintaining organizations--mainly in merging different wordings and abbreviations of the same place--this is less trouble than you'd go through to prevent these contacts from being created.

Like the proverbial tree falling in the forest, a contact in your database doesn't make a sound if nobody's searching for it.  Mark your important contacts in ways that you'll find them, but a contact that's just in there as an employer won't clutter up your work unless you're making grossly over-broad queries.

(Besides, who knows if they'll end up as the employer of other contacts?  You might consider a workplace giving program.)

Most importantly, don't let the mere existence of a contact in your database signify anything to you.  Segment your data based upon location, activity, opt-ins to lists, and so forth.  If a contact is exclusively an employer of another contact, with no further information, they'll never have any of this other data--the information that you should really be basing your communications and analysis on.

In short, don't fight this core feature of CiviCRM.  It's innocuous, and it would be confusing and/or expensive to work around.