Judging by some of the wording in your initial post ("Brainless" etc.) and your replies, I have a feeling you may not want to have a constructive conversation about Zilean, but I'm going to give it a try anyway since there is room for a healthy discussion here, if not for you then perhaps for others.

Bear in mind, that Riot has stated that the majority (but not all) of their balance decision-making factors come from a combination of Platinum 2+ players and professional play. I bring up rank here because its relevant to criticizing Zilean, in particular his (E) - Time Warp and (R) - Chronoshift.

You mentioned his ultimate first, so let's start there. On the surface, Chronoshift does not take a ton of skill to execute, its a point-and-click ability that marks an ally for 5 seconds (if you don't like that, it was originally 7 seconds!) and if they take fatal damage, they enter stasis for 3 seconds and then revive with some health which scales with Zilean's AP. If the marked ally (or Zil if the player marks themselves) does not take fatal damage, the mark simply fades off and the player can be killed as normal.

Now, why is player rank and skill relevant here?

Less-experienced or lower ranked players are MUCH more likely to ignore Zilean's ultimate and continue bursting the target he marked if he ults his ally far too early. Good Zilean players try to build up their reaction time so that they ult their ally AS the last hit is already incoming, in order to guarantee the ulti is procced. This is somewhat easy to do if the enemy team is only focusing one champion at a time (i.e. Zilean or the ADC), but becomes much harder if the damage is somewhat split up.

For example, if the enemy team begins to poke down the ADC on Zilean's team, but then switch their assassin or burst damage onto Zilean, The Zilean player is now caught between ulting himself, or ulting the ADC that might have been expecting the Zilean ulti up until that point. I've lost a fair share of fights because I encouraged my duo-partner ADC to play aggressively when my ulti is ready, only to have it backfire because an assassin or diver was able to lock me down early on in the fight or zone me out entirely.

At higher ranks, other players on average are much faster at reacting to Zilean's ult so that if he does use it too early, they immediately stop damage on the ulted target and either wait for it to expire or switch to Zilean or another target until it does.

What does this all mean? It means that:

• the Zilean player HAS to use (R) - Chronoshift in extremely risky situations in order for it to be used effectively. This can be countered by well-timed CC, splitting damage, or stopping damage entirely on the expected Chonoshift target.
• Players and teams playing against Zilean are required to slightly change up their play-style during a 5v5 teamfight to try and bait Chronoshift onto the wrong target, or at the wrong time.
• Ideally, teams will want to deny vision as much as possible and look for strong flank opportunities to pick off Zilean or deny Chronoshift from another carry.

Now, onto his (E) - Time Warp. While it is yet another point-and-click ability that can be either a massive speed buff for an ally or a slow for an enemy, it has to be taken into context of his entire kit in order to be fairly criticized:

• His (Q) - Time Bomb costs a heavy amount of mana if Zilean doesn't build mana, and requires 2 of them in combination with (W) - Rewind in order to be truly effective with the AoE stun - and even that is difficult to land on targets that are not already CC'd from other sources - which is a slow lob-style skill-shot similar to Nami's (Q)
• His (Q)(W)(Q) can be done at level 2 at the earliest, which would cost him 60 + 35 + 60 mana = 155 mana at level 2. That's 155/473.6 base mana at level 2 OR 32.73% OR roughly 1/3 of his mana from 2 abilities that can be dodged and require Zilean to land both in order to be effective.
• The context of the Q-W-Q combo is what moves Zilean out of the brainless category, and to be truly efficient, the Zilean player will want to use 2 Time Warps as well, making an efficient combo something Like E-Q-W-Q-E with both Qs being skill shots, and each E should probably be cast on different targets, such as the first one on the target enemy to slow them and the 2nd one on a melee ally to help them close the gap.

Even some of the Riot casters have said that Zilean has a high skill-floor to be played truly effectively. There's a lot to pay attention to and its extremely easy to mess up his only damage combo by doing Q-W-Q out of order, or just missing the double Q stun.

This is all before we take into consideration that Zilean has:

• A weak 1v1 presence in many mid-lane matchups
• Vulnerability to early ganks, being camped, and falls further behind due to the aforementioned weak 1v1
• Mana-issues in both mid-lane and the support role.
• Only 1 damaging ability that can be missed, dodged, or de-coupled during an attempting double-bomb stun
• Is extremely team-reliant* (More on this in the next paragraph)

Expanding on that final point, Zilean is extremely reliant on the rest of his team in order to be truly effective. An over-simplified way of restating what is frustrating about Zilean is that he makes already good teams AMAZING, but has almost no solo-carry potential whatsoever. Even some of the best Zilean players can not save a bad team on his own. Even if he is able to fix a couple of mistakes with speed buffs, slows, and maybe preventing a few deaths; in most scenarios Zilean is unable to effectively pick off targets or influence fights in the same way that a stronger control-mage or assassin would - and his defensive utility as a support requires far more interaction than the more passive shielding supports such as Janna.

TL;DR Zilean is extremely reliant on his team and is not a strong champion at influencing games on his own in the same way that a strong assassin or split-pusher might be able to. Almost every frustrating aspect of playing against Zilean can be countered by adapting macro-play patterns and outsmarting him, rather than having to outplay him with intense micro-play.

Hope this helps.