If your goal is to be able to do a solid straight handstand for 10 seconds every single time, you probably don’t need to train Endurance. However, most of the advanced skills require you to spend a decent amount of time upside down (like going from straight to straddle to tuck then back to straight again OR going from straight to straddle to one arm then lifting the other arm, etc.) so you need endurance for these skills.
If your endurance is bad, your strength will fade quickly and you will soon find yourself without enough strength to hold a good handstand, let alone execute positions that are even more physically demanding on your body.
That being said, you don’t want to focus on training your ‘max time’ before you have good foundations in place. Doing this can easily lead to discomfort or injury because your body might not yet be ready to be put under the strain of doing handstands for such long periods of time.
Pushing your body past what it’s capable of AND doing it with bad technique is a great way to injure yourself. Injury is almost always caused by changing your environment too soon and/or too much (discounting accidents, falls, etc.)
So, pushing your body to increase your ‘max time’ endurance holds before you have good foundational technique OR pushing your body to increase your ‘max time’ too quickly, is going to increase your risk of injury and this could take you drastically away from your goal.
Many people think that the best or only way to train endurance is by doing a handstand (freestanding or against a wall) for as long as you can, over and over again. This does work but there are smarter and better ways to train your endurance.
It’s better to train endurance by taxing your body by changing certain variables such as volume, intensity, duration of execution or rest, etc. WITHOUT compromising technique (to a certain extent).