'Sky Pencil' holly, it seems to rather often fall open instead of remaining strictly columnar. You will either have to rig up some kind of a support system that holds them together or remove and replace with another variety of shrub.

If I get a support beam, will it just remain dependent on the stake forever?

The other two next to it aren’t having the issue.

Would trimming off all the drooping branches how back stronger if I cut them off?

Yes, you will have to provide support indefinitely - there was another recent post showing a planting of much older and larger examples with a fairly high percentage of them where pretty much all of the top had flopped open. And the other two you have look like they may be in the process of opening up also. So that if an entire branch is cut out every time it starts to lean away from the center of the specimen you are probably just going to eat away your plants until little of each is left. For instance with the one you are asking about now if you cut out that whole branch to the left that will be nearly 1/4 of the top being taken off in one move.

I wouldn't stake. Instead, loosely tie the branches together using jute or stretchy landscape tape. May need to be replaced periodically but far less visible and obtrusive than staking.

Much the same principle involved in tying up arborvitaes to prevent winter splaying from snowloads.

The several I've seen that look good were discretely trussed up. I think you might have to accept that's the cure. Catalogues and nurseries do not generally advertise a plant's shortcomings which often present as the shrub/tree matures. It is my experience that as branches grow, thicken, reach for the sun, there may be structural issues that aren't a problem with a smaller plant. The two other posters are much more experienced 'growers' than me, but I've got a garden full of shrubs and trees that need corrective pruning /treatment because I didn't know what I was buying or how to maintain them over the last 10 or 15 years and wasn't aware that everything was growing, including the maples which cast increasing shade.

I have this plant. Ilex 'Sky Pencil'. Here is a recent photo of it in the background of this photo.

It is upright. Mine is about 10ft tall now. It started out about the size of your largest shrub. Some of the branches loosen up a little, but I'm not concerned about it. if some of them really separate from the main body and it bugs me, I'll cut them off, but I haven't done that in 2 years. I tie it up with string every winter so it is not damaged by snow and ice. I tie it loosely around the base with nylon and then tie string to that and just wind it up to the top. I just cut off the string a week ago. It's been very windy so I left it on longer this year. I don't leave the string on all summer, because I feel that the shrub should tighten up on it's own having to cope with wind. Isn't that why they now advise us not to stake young trees? I will try to take a closer photo.

I do the same to two Arborvitae that are in pots that stay outdoors all winter. Someone who did some pruning for me, managed to stake the smaller Arborvitae in the pot and then tie them without it being visible and I leave it that way year round. I don't really need to, but, I really like the neatness of it.

I had two of the Sky Pencil. They were in an alley on the north of my house between the house and the garage. They seemed to be doing just fine there, but I moved them out. At first I added them to a bed that had very little sun, but I had that problem, that they were drooping and the branches were separating to some degree, I moved this one to a half sun location and it's done just great there. This is year 3 since I moved it to this location. I don't know why they did okay in the first location which was shadier than the second, but that's the way it evolved here.

I thought the other one, really struggled after I moved it the first time and I shovel pruned it. When they are younger they can look a little messy, but I've seen them full grown at a local nursery and they are upright. Not as narrow at the base, they widen out a little but taper into a narrow top. I enjoy mine. I like that exclamation point in the garden.

This is the first year that I'm seeing it all settled in and starting to put on more growth than it has before. New branches from the base and lengthening of those that were there. I just added some Hollytone around the base, so I'm encouraged that it will eventually become like the mature versions I've seen at the nursery. I like it right now, just the way it is too.