It depends on how you feel the fiction plays out. Is holding a spell already cast a relatively painless tactical choice or are you barely able to contain the arcane energies you've called into existence but refuse to release until they escape harmlessly?
In many ways it would be good to have an idea of the designers conception so each table doesn't have to negotiate aspects such as this. On the other hand, it allows table play to map to table desires by not providing a default answer that then needs to be overridden. In my view, the first option leads to simpler and more even play since the decision can have an effect on tactical balance.
Well, we can examine it logically by its effects.
Consider this scenario:
The party are waiting to ambush a band of orcs.
The party frontline fighter/face stands out in the open to meet them. The rest of the party hide in bushes.
The archer readies an action to shoot at the first orc when the attack signal is given.
The wizard readies an action to cast Magic Missile at the three closest orcs when the signal is given
The orcs do not arrive during the first round, they arrive during the second. What happens?
The rules as written say that the trigger a Ready action creates only lasts until the start of your next turn, so both triggers vanish. The Archer can spend her action to Ready the same trigger again, and all carries on as normal. The mage... has already spent the spell slot to cast Magic Missile. It's gone. The spell is not yet wasted, though. I see three ways this could be ruled:
1) You rule that the spell fizzles. That would mean that Wizards have a tactical nerf compared to pre-5e, when they could ready actions with the same tactical power as other classes.
2) You rule that the spell must be cast using the Wizard's action or it is lost. That's still a tactical nerf, and in the example makes the wizard complicit in his own nerfing (since he either has to waste the spell slot or ruin the ambush).
3) You rule that the Wizard can keep the spell going and Ready the same trigger. That, to me, is clearly the fairest and best ruling, since it preserves pre-5e tactical utility.
Given that the ability to hold a spell partially-cast is Concentration - and there are proper rules for how that interacts with other spells - it's a very small step from 3) to allowing the wizard to cast another spell while keeping the first one imminent.
It's even nicely balanced - even if you had two readied spells, you could only actually complete one per action, and since you need to Ready to use a trigger you can't complete both of them in one round. There's no way to break the "minimum one action per spell" limit.
Allowing this sort of thing is wonderfully thematic - in fact, I think this is one of the reasons they ruled it this way. I'm imagining playing - say - a half-orc battlemaster fighter (could go Eldritch Knight, but the concept doesn't need any more magic than the cantrips), maxing out intimidation. Take the arcane initiate feat (or whatever the full version gets that's equivalent) and the fire bolt cantrip (and Shield as my once-per-day spell), then start partially casting firebolt and threatening people with my glowing hands.
It would work especially well during an interrogation - waving a glowing, smoking readied fire bolt in the face of the tied up enemy and explaining that they should start talking now...
) 
