If you can ready spells outside of combat, combats will start explosively; if you cannot ready spells outside of combat, this will have little impact
The way the ready action normally works is that it allows you to delay the casting of a spell. (You lose your action to cast, but can now use your reaction). Changing this to an indefinite holding time allows for a spell to be readied before combat starts this giving them an extra spell.
This also allows a party of spellcasters to co-ordinate their spells as much as they want, potentially ending combats immediately as multiple readied spells trigger by something such as "when I first see an enemy" and so they would all be firing spells before the first person's turn.
Combats start immediately with multiple reactions and lots of spells which is likely to result in a lot of immediate reductions to 0HP for combatants.
We also run into a problem depending on how we resolve the reactions. If we don't have them resolve simultaneously and the readied spells deals damage, the first fired spell would cause concentration saves to happen and so people may lose their readied spells. If this happened it's possible only one side/team actually gets to use this tactic, and so readying a high damage spell will always be a way to swing the combat drastically in your team's favor.
This tactic would be quite unfun for martial combatants as they can't do anything. And spellcasters may start combats losing their spell slots as the enemy team bombards them with damaging spells that they can't do anything about.
If you did not allow for readying spells outside of combat this would create little change in the dynamics of the game because of the action economy cost.
Casters would lose out on their action each turn they maintain the spell as the spell would be subject to the long casting time rules:
When you cast a spell with a casting time longer than a single action or reaction, you must spend your action each turn casting the spell, and you must maintain your concentration while you do so...
So if they wanted to keep holding the spell they would have to be spending successive actions to do so, this is a significant balancing factor as it limits them from using that action on anything else.
This adds the ability not to lose your spell slot as easily as the readying a spell section states:
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs. (Players Basic p. 72)
This means that you have already expended a spell slot in this casting, and the change to how long you can hold a spell allows you not to lose this slot immediately when your next turn comes around.
This allows for some options such as multiple casters each readying a spell so that they all pile up after some specific thing occurs (perhaps after the creature is knocked prone) as you can now wait any number of turns for that trigger to occur instead of just one as with the usual rules.
Ultimately I believe this would have little impact as it still eliminates the casters' actions as they must use them to maintain the spell.