As I mentionned before, I reaaally have a hard time envisioning the feature, considering the case where you manually choose your position in the queue, being anything other than "cheating" during a fight. UNLESS the IA is able to also delay their turn... Which would lead to insanely boring situations were everyone delay their turns until full AP.
I think it should not be manual, but automatic, calculated on the characters stats. Maybe a very fast character could virtually choose when he strikes, because each time you delay their turn, their position in the queue move just after the next one in line ( A B C becoming B A C and then B C A ). On the other hand a slow or encumbered character would be put further away in the queue, down to last position before the next turn. That would maybe makes sense for, say, a healer, when suddenly the speed stat becomes way more interesting, especially considering there may be cooldowns on their heals ( free bridge to the "cooldowns and AP are redundant" discussion ). On the other hand, it may not be a good thing for a healer to put too much points into the Speed stat, so, decisions, decisions !
At the end of the day, I think this would somehow mimic how turns work in Heroes of Might and Magic. I'm don't quite remember, though.
The whole point of having a "manual delay system" is giving players agency. It's not cheating simply because games that use this system are balanced around the idea of a flexible initiative queue. Players ARE SUPPOSED to take advantage of smart sequences of actions: if they don't, they lose. End of the story. The games I mentioned before are great tactical games precisely for this reason: they reward players for being smart in a way that games with static initiative (or semi-static) can't.
As for Heroes games, see below.
And, why should delay not allow it?
If the order is reversed, let one wait... and you can do it?
You need to give a bit more details or an example of such a happening where the current system is insufficient.
And "I might die, so I want a position in the middle to zip potions, but a little later than the start to see how much HP I will loose" is not an appropriate answer
Details? Here they are: D:OS already features many interesting skill combos (or skill+environment combos). 2 Bitter cold spells freeze your enemy, a wet mob is more vulnerable to a lightning spell, you can throw a barrel near an enemy and then send both to Mars with a fire spell, etc... Delaying your turn till the end of the round doesn't allow you to take full advantage of all these combos: if one or more mobs have the opportunity to move before you complete a combo, odds are that they screw your plan.
In HoMM creatures have a place in the turn order based on their initiative and intiative modifiers. Then, they can wait to act after every one else, or pass to gain defensive bonuses. So that's basically how initiative works right now in D:OS, except there is no "pass to buff defense" option.
As much as I love HoM&M games, they are not a good example here. They are great games when it comes to the strategic layer, but tactically speaking are just average. You can't simply compare their combat system to Jagged Alliance's or ToEE's.