Yes almost always the fare for upgrading is higher than the main cabin fare on offer. Sometimes it can be the same when the main cabin fare is already in those higher fare buckets like YBHK when cabin is getting close to full or they are zeroing out cheaper fare buckets to force people to pay higher regardless of loads. It’s the same situation for all types of upgrades. You see the pricing when you select MVP, gold, 75k, miles etc with mvp being the worst since it requires the highest fare buckets to be eligible for instant upgrades if U space is available.

It makes the most sense to not buy the higher fare to use a guest code if there isn’t U space available at purchase. If a U spot opens up later, it is possible to reissue the ticket in the higher fare bucket through reservations but there’s no guarantee it’ll be at that price you could have had when you originally bought the ticket. You could buy the eligible fare initially and wait for space to open but there is no guarantee and it isn’t automatically applied like it is for the elite upgrades.

As a 75k for example, I’ve bought the eligible fare when it hasn’t been much more than the lowest main cabin and I’ve been upgraded at random times before departure date like 2 months ahead or 2 weeks ahead. U space does open up but any elite waitlisting on an instant upgrade fare will snatch it up quickly and automatically.

For your daughters situation, I would have her buy the higher fare initially if the flight isn’t too far out and has plenty of seats left in first and not a lot of premium seats taken (could be golds) & you will be monitoring the flight closely either by constantly checking or setting a U alert notification on expert flyer. If she’s an elite, not all is lost with paying more because she does get prioritized higher in her elite group based on the higher fare bucket purchased so a complimentary upgrade might happen anyway.