I think I would reframe the OP less about cost cutting and more that the company has an unrealistic cap on salary. Would be interesting to see where geographically your experience was. Having worked in the Midwest the problem I have found is that the population wanting to live in the Midwest is small and then when you are trying to recruit top talent it is even harder. You would need to pay more but then most companies do this analysis where they say the median level 1 junior tech salary is x for this region. Which on face value is maybe ok but then you look at the job market and there is low to no real tech jobs. To hire smart people you are asking them to move to a place that has less to do and no interchangeable market for their talent.
In software, groups of people (teams) have value far more than individuals. You need a large pool of talent to reliably build good teams. This includes some amount of the very best people world wide.
These people gravitate towards big cities where they can earn more, access more amenities and work with other top talent.
Remote could have changed that, but it seems to have fizzled for now.