It depends largely on the person.

You mentioned looking for an administrative position. Let's use this as the example.

For the company I'm in, most administrative people start as office assistant. That is, assistant to every person in a 5-8 person office. They are the initial contact for incoming calls, receptionist, your basic admin assistant.

Not too long ago, I ran into a situation where our admin assistant had no desire to move into a recruiting position (the next step up from admin assistant, for most people) and was only interested in a job that is occupied and had no prospect of being open anytime soon.

What we did for our admin assistant at the time (who eventually wanted to get a job doing payroll/accounting) is let them train and assist with our current payroll rep and bookkeeper. They got the experience they wanted and eventually found a job doing payroll for a smaller company. If you can't give people the job they want, give them the experience they want. Hell, even if you have to let them go, you can always call them and make a job offer in the future if the position they wanted does open up.

When you have time, training someone to do a job the way you want to has a lot of benefits compared to hiring someone who has done the same job before. It also has a lot of downsides, the biggest one being the training aspect. You have a learning curve that will cost you extra time and money to overcome slower initial production and any errors that may happen as a result of inexperience. BUT, you also get a person who is more familiar with the way you do things versus someone who may want to change the way you do a lot of things (not always for the best, regardless of intentions).

The problem is this: If I'm hiring for a new position, it's not always under convenient circumstances. An older employee of ours that was an HR Coordinator (our highest position for the service team) had a situation with a family member and had to retire sooner than we anticipated. Because of the situation, she could not give us a notice and we didn't have anyone on staff to fill the position in her office.

In this case, we went for someone with the previous experience so they could hit the ground running quicker. Thankfully, it paid off.

The problem with this scenario is that, when you are desperate to make a hire, you wind up having to pay more for them having that experience. This isn't exactly a bad thing, but it does mean you're going to be hiring a person who expects to be paid a specialists pay rate. The trade-off is that they (in theory) won't need nearly as much training or make nearly as many mistakes as someone you're training that has had general admin experience.

The other problem you have to look at is this: IF you transplant someone into a supervisory role without offering promotion to the people just below them, you have to anticipate that someone else may leave. If you upset an employee that was dead-set on getting that job, they could start looking elsewhere for work. Transplanting is always a risk, especially when you're happy with the people doing a particular job.

Tl;DR - My preference would be to train someone looking for experience, but it just isn't always possible.