This was a nice way to do it because my salary has always been monotonically increasing, and I wasn't offended that my increases were small for a few years because I knew why it was happening.
At Google they just openly adjust your salary if you move between cities; move from NYC to Atlanta and you'll take a bit hit, move back for the reciprocal instant raise.
Regardless of the rational and pragmatic reasons behind salary adjustments for cost of location adjustments, a double digit X% cut would be very demotivating for most people psychologically.
This has been SOP at big tech companies for years. If you choose to move to a cheaper location, your salary will be adjusted to the new market rate.
I know plenty of people who have gone through this and nobody felt demotivated. They all chose to move and were well aware of the salary cut when they made that choice.
Very very few people would not be expecting a location adjustment to their salary with a major relocation. Especially when that relocation is entirely for the benefit of the employee, not the employer.
That can't be helped. If I had a 100k size org, I wouldn't hesitate to set (overall) compensation targets at regional top prices with instant adjustment.