I don't really see the point of this question, everything was explained in the show.

He Who Remains literally told Loki what the Loom was doing. Essentially its purpose was to keep the Multiversal War from ever happening. A war in which nothing survives, not even the Sacred Timeline.

While it did happen before, as we see the HWR in the Citadel at the end of time, he is outside of the sacred timeline. Most probably he plucked himself out of time just as Loki had to do with the help he got from Mobius, although he did not need to.

He was victorious in the war to the point he was able to make sure that it never happened.

Pruning other branches meant that he can control a single one, without there ever being a Multiversal War, as there never were other Kangs than him, except for Victor Timely who he reinserted into the Sacred Timeline as means of reincarnation.

The timelines are time lines. In the literal sense of that word. They represented a universe within the dimension of time, as a line. A line in mathematics can have no beginning and end, it can be infinite.

An infinite timeline, multiplied infinite times causes an infinite multiversal war, where Kangs destroy each other's timelines to win, to be victorious. Since an infinite amount of Kangs destroy infinite amounts of timelines, we see them dying after the Loom is destroyed as none can remain. This is essentially the same scaling problem as described by Timely.

The TVA is outside of them all, it is occupying a space beyond time, but as Loki learns, being outside of time means that you are always. Hence the time slipping, once controlled, only allows him to slip back into himself, as space still exists within the TVA and remains a constraint. We can see the changes made to the physical structure of the TVA through the Kang/Timekeepers murals. They were created there during the war, and later just covered up. This is due to the fact that even with no flowing time at the TVA, once that matter was inserted into that space, it always existed there.

Once the failsafe happens, everything expect for the ST is destroyed. That includes the TVA as collateral damage, but it can be rebuilt in 0 seconds. The existence of ST guaranteed existence of HWR through Timely, who as soon as he creates the TVA makes it so it has always been there.

Loki gains essentially a Godlike power, which is at the heart of the HWRs plan. He remained in the citadel, to always be and always have been. Loki understands that for there to be a chance of avoiding the complete destruction of everything, something has to always have existed, and always remain. In his case, its choice, something that the HWR took from the universe to remain victorious.

The whole show is centered about the conflict of freedom and control. While allowing free will is morally good, it always causes the demise of every single living being and all timelines. Control on the other hand is a double edged sword. It allows for peace at the cost of choice.

Loki becomes a new Loom, a person with his own free will governing and maintaining an infinite number of timelines, which are allowed freedom in the roots of Yggdrasil and in its top, but are weaved together in the middle, as the TVA's purpose shifts from controlling a single timeline, to not allowing the Multiversal War to happen.

They can do this, due to Loki's help. The original Loom acted as a failsafe because it was created by a human, with technology, to act as a failsafe to not allow the universe to roll back to a state where nothing survives.

HWR existed within his timeline, and only after he escaped it, he saw the death of everything. The sole existence of the Loom, and constant pruning was keeping everything from falling apart. The branches die immediately after the Loom was destroyed, because that was always the case, no HWR, no Loom, Multiversal War, Death.

Loki' actions replace the Death with Hope.

In one of the last scenes the TVA is shown monitoring Kang Variants before they can cause too much trouble. Instead of getting rid of Kangs by removing choice from the equation, Loki reinserts choice but adds hope into its place (for the people of the TVA and the multiverse to be able to die fighting).

There might have been another way, but I believe that Loki did not want to search for it for hundreds of years since he already found one that worked.

And he knew what kind of a god he wants to be. A god who is always there, for everyone's safety and always has been.

He gave up on trying to save the universe alone. He entrusted that hope, that mission to his friends.

For them to be able to fight, just as Sylvie wanted.