Skimmers are mainly used for saltwater aquariums not really for freshwater ones
I'll add to what
@MJQMJQ has said here as skimmers come in 2 quite different forms which can be categorised as 'Protein skimmers' and 'Surface skimmers' which is how I will refer to them.
-Protein skimmers are primarily used in marine aquariums and work in quite a different way to a surface skimmer but they remove what's essentially waste food and fish poop.
-Surface skimmers are mainly used in freshwater aquariums to skim the surface of the aquarium to remove any surface scum build up; oils, food, plants and the like but in a very different way.
If you're interested have a Google!
There are then 2 types of surface skimmer; ones which are independent and electrically powered and ones which rely on the filter to cause suction to pull in the wastes like you are using, both essentially do the same job.
Any opinions on how important skimmers are?
I find I do need to use a surface skimmer to keep things clean on top, you will hear many people on here saying things along the lines of
'something is out of line if you need to use one' or similar but you will find many people on here that do use them and if you look at tanks from places like aquarium gardens you will see they are using them too - I'll let you be the judge.
most people seem to put the lily pipes/skimmers near the front too, which in my eyes detracts from the tank
Just had a look at the video of your aquarium, good effort.
I would say you have a big fault with the position of your inlets/outlets as they are both facing each other, it would be better to have one set at the front and the other at the back to create a circular flow, this can also dictate which way around our inlet/outlets go in sets. At your back left you have your outlet nearest the front and inlet behind it which I would suggest is the opposite way around to have things. (inlet goes into filter outlet comes from filter to aquarium) If you were to swap the back left around then move your lily pipes to the front on the right then this would work. Does this make sense? - just think circular flow; one pulls flow in, the other forces flow out
I'm not a fan of looking at them either so try to hide things as much as possible, I'm not a huge fan of glass either as it can show dirt up very easily despite keeping them clean and you do still see them. I've used stainless steel in the past, simply as I prefer the look.
A 45cm cube is small whatever inlet/outlets you use and worth just looking around to see what other people have done in the same situation.
I don't have an answer to your question going forward but hopefully some of what I've said will make sense and can improve performance in your existing aquarium, if it doesn't make sense then just ask.