Companies do this, but the fact is that your compensation is supposed to be based on the work you do now, not the work you used to do. They agreed that $60K - $65K was in the compensation range for this particular position.
If you accept the offer, they will be underpaying you to the tune of $10K+ per year, or 15%+ under the appropriate wage. Not sure why what you are currently making comes into the picture, because that's irrelevant to the new position. Basically they are saying they are going to punish you for having an employment history for them, because if you were an outsider coming in and they could not peek into your compensation, you'd be getting paid the range you originally discussed. Who says "Thank your for being a valued and loyal employee. Now bend over...." - rhetorical question. Your new employer is who, obviously.
There's nothing illegal about trying to grossly underpay a worker for a job and low-balling them. There's no expectation of privacy about your current wage from your employer (who pays that wage), so there's nothing illegal about having the information and choosing to use it. There's nothing illegal about you declining and starting to look elsewhere, either. There's nothing illegal about you accepting the offer, but I can't say it's particularly smart to tell your new employer that you're willing to be a doormat for them. The idea that you'd cave in and accept a grossly inadequate offer, and that this will somehow position you for a raise to a fair and equitable wage in the future is kind of an unrealistic interpretation.
The company already has shown a willingness to underpay for arbitrary reasons, and to try and strong-arm you into it (ignore the counter-offer, while offering no legitimate reasons). Why would you think that would change, at all, and why would you think it would change after you rewarded their behavior and showed them it will work on you?
Stay put and find a new job where you are, unless you think the job market is better in the new location, but if you decide to look for a new position in the new location, make sure there aren't strings attached or claw-back provisions for the relocation money.
It might be better to accept, because declining and staying at your current wage might be an indication to them that you might be looking to leave, and they might drop the hammer on you if they can line up a replacement, so if you decline and decide to look for something else where you are (if you like where you are living), maybe give a reason (only if asked) that the differential isn't enough to entice you to leave the community you like so much.
Also - relocation money. Some companies directly pay for the relocation. In this case, it looks like they are giving you a bonus for that relocation. If your relocation costs are anywhere near $7500 you get screwed in the deal, because you pay FICA, federal and state taxes out of that bonus. Also, under the new GOP tax plan, you can no longer deduct moving expenses if you itemize on your federal taxes (as of January 1, 2018), so there's no re-couping that. Make sure you don't view that relocation bonus as $7500 to pay for relocation. It will probably be closer to $4000 in real moving money. A standard agreement I used to see was where they'd give a bonus for the typical estimated cost of the move, plus a "gross-up" so the after-tax net winds up covering the move. If you wind up losing money on the move, that's another consideration when evaluating the offer.