Would it be possible to build a 10 000 feet skyscraper?

Sure why not

It's quite possible to do it.

The reason we have not done it, or even exceeded 3000 ft high so far, is that it become exponentially more expensive the higher you go. It's just cost too much to do so, and you could never recover in rents or selling condo's even a fraction of the cost to build it.

In 1956 Frank Lloyd Wright released the design for a "mile high (5280 ft)" Skyscraper for the Chicago area "The Illinois building". It could have been built with the technology that existed in those days (no special crane designs needed).

https://lynceans.org/wp-content/uploads/2020/05/Frank-Lloyd-Wright_-1956-Mile-High-Skyscraper_R1.pdf

However, retrospective design analysis indicates that the building would have needed tuned mass dampers to control the sway to levels considered acceptable to people that would occur during certain weather events. Yet, it would have been structurally sound (even if it swayed in the wind).

There would have been space in the mile high building to install such dampers.

The first use of tuned mass dampers in sky scrapers occurred in 1978 when it was discovered that the new Citycorp Center building in NY City was swaying more than was comfortable for the construction workers. The Design Architect quickly designed the tuned mass damper and had it installed - and the sway problems were solved (and now tuned mass dampers are standard on all skyscrapers).

I note that application of such a tuned mass damper for tall buildings was theorized and published in 1949 as a way to control sway of buildings. As such, it is likely that Frank Lloyd Wright and his engineers would have known about the idea - just not had never seen where it would apply. Perhaps the tuned mass damper would have first been installed in the 1960's if the mile high Illinois building had been built.

The current tallest structures in the world and planned structures have all taken design cues from the 1956 Frank Lloyd Wright mile high tower plans.

Recent economic reviews have indicated that all of the most recent very tall skyscrapers in the last several decades have an actual negative economic value (they cost more to build than they are worth as an investment asset).

It is worth noting that there were plans to build a 1 km (3281 ft) building in Jeddah, Saudi Arabia ("Jeddah Tower") and construction stated in 2013. Construction was suspended in 2018 with the building structure about 1/3 its design height, and there are no current indications that this building will ever be finished.

Idk bout with todays technology but yeah eventually. Youd have to built special cranes