[AOI][TOTK] The shrines of light connect back to Skyward Sword.

In TOTK its said that the shrines are, even up to current day, imprisoning and purifying an ancient evil. This isn't in reference to Ganondorf, since they come before. With Age of Imprisonment out, we now know that if left unchecked, this "evil" spawns in the Shades.

Demise is the origin of monsters. For a long time we've thought that Ganon has been spawning in monsters as well, but actually what we've been seeing is consistent with Demise being the origin. There's something of him left in the world that continues to spawn in monsters, it is this thing that the shrines of light were combating. Take a look at what the TOTK Masterworks says on how the Demon King seems to spawn monsters:

闇の力により生み出される「瘴気」は触れたものの体力を奪うが、魔 物や魔王自身には影響を及ぼさず、むしろ身に纏うことで実質的にその 力を強化している例もある。たとえば、地底の魔物などである。また、 魔王は大量の魔物を生み出したとされているが、ラウルらが破魔の行脚 で封じていた〈邪〉からも魔物が生まれていたことを踏まえると、魔王 は闇の力で「魔物を生み出した」というより、「邪を強化」することで魔 物が生まれる行程を促進し、瞬時に多くの魔物を出現させたとも捉えら れる。

Coming into contact with ‘miasma’ which was created by the power of darkness drains physical strength, but it does not affect monsters or the Demon King himself, rather there’s examples that clothing his body in it substantially strengthens his power. For example, the various monsters in the Depths. Also, considering a large quantity of monsters were created by the Demon King, but also accounting for the monsters that were born from the (evil) that Rauru and Sonia sealed during the exorcism pilgrimage, rather than saying that ‘monsters were created’ by the Demon King’s power of darkness, it’s possible that the Demon King accelerated the birth of monsters in an instant by ‘strengthening evil’. 

This suggests that the Demon King isn't actually spawning them himself, he's actually strengthening this "ancient evil" that the shrines have been keeping imprisoned and purified.

The Masterworks also suggests that Link taking the Blessings of Light may have consequences:

勇者の行為は許されざるもの?

Are the deeds of the hero inexcusable? 

ハイラル各地の「破魔の祠」で体内の邪気を払っていったリング。 勇者が本来の力を取り戻す行為は世界にとっても好ましいことのはず だが、この行為を危険視する声も挙がっている。祠の上部から噴出 していた浄化の光の渦が消失しているのだ。祠の役割が判明した今、 「これは破魔の浄化装置が停止したことを意味するのでは」という危 惧が生まれたのである。現在のところ被害報告などは聞こえないが、 再び邪気が現れかねない。今後の 経過を注視する必要はあるだろう。

Link dispelled the evil spirit in his body in ‘shrines of exorcism’ in various places in Hyrule. The act of the hero recovering his original strength should be a desirable thing for the world, but voices regarding this act as dangerous have also risen. This is because the vortex of purifying light that erupted from the top of shrines has disappeared. Now that the role of the shrines has been established, this has given birth to apprehensions that ‘this means that the exorcism purifications could have ceased.’ At current time no reports of damages have been heard, but evil spirit may materialise again. It will likely be necessary to keep a close watch from now on. 

This isn't to say that any conscious part of Demise is still around, but his hatred continues on as he says at the end of Skyward Sword. If anything is the direct result of his curse, it is this. But so is Ganondorf, since he mentions that an "incarnation" of his hatred will also appear. Two things, his hatred and an incarnation of his hatred.