I'd like to know what hiring personnel would think of a applicant who
would willingly take a pay cut to work for their company.
I'm assuming this is a temp/contracting job.
Hiring companies wouldn't know or care what your rate was at your last gig.
The hiring manager usually starts with an hourly rate in mind (a budget, basically) for that position. They then contact the agencies, send the job description and details, and indicate how much they are willing to pay for the job.
The agency then goes down their list of qualified candidates trying to find a few that fit the profile at the budgeted cost. It's in their interest to find at least a handful of viable candidates and get their resumes to the hiring manager quickly. Usually a manager fills the position quickly.
A good agent will tell the hiring manager of candidates that are qualified but requesting too much money. The manager can sometimes "bend" their budget and pay more. But often the job requisition would need to be rewritten, several levels of approvals would need to occur, agencies would need to be alerted of the req change and that would all take time. Honestly, it is seldom needed, since there are usually so many viable candidates willing to accept the budgeted rate.
A good agent might then choose to tell a candidate that they are qualified but are asking over the budgeted rate and offer them the chance to accept less and be considered.
So even if you go in to an interview and say "You know, I decided that I would accept less than my usual rate because I'd like to work here." that would seldom impress the hiring manager. For temp jobs, they usually aren't looking for stars, just someone good enough and timely enough at the budgeted rate.
If you strongly feel the need to stick to your desired rate, then go ahead and do so. The hiring manager may match your rate, the agent may accept a bit less in order to help you, or you may just need to move on to a different gig (the last being the most likely outcome).
If you really want to work at this company and are willing to accept the offered rate, then do that. But don't expect that your willingness to compromise on the rate will be a big factor in selecting you. It may very well help you get an interview, but that's about it.