I haven't done this, so cannot answer from experience.
Do you think this is a good idea?
As usual it depends on the group. It is worth going to the apparent reasons for the way summons work in 4E, to decide whether these issues would affect you and your players:
In 4E there is by design a strong balance factor maintained between PCs, irrespective of class. This attempts to ensure that all players get equal opportunities for "screen time" and effectiveness in battle. A powerful summoner is going to look maybe twice as effective as other non-summoning characters in combat, because the companions are direct result of that PC.
A core resource in 4E combats is your number of actions. That is why Action Points are such a limited resource, and the reason why getting side-benefits on Minor actions is useful etc etc.
4E combats are quite slow, and the pace slows down for each action that needs to be described.
Un-restricted actions for summoned creatures are something that makes the Druid (or other summon specialist) characters top-tier classes in edition v3.5 - all else being equal, it can be a game changer in terms of PC-to-PC balance (after level 5 or so, a Druid can be equivalent to 2 or more Fighters)
The above are IMO drivers for the more restrictive summons powers in 4E. Daily summons powers often add small extra attacks, because Daily class powers provide encounter-long buffs in many cases. But adding that effect to constant companions enlarges the turn of players who have companions, and skews balance in favour of classes, feats and backgrounds which grant them.
If you have power-players in your group, they might pick up on advantages from having more actions, and you will find yourself running slow encounters with 10 sets of actions on the player side.
If your group is more RP heavy, then it would be less of an impact. But the counter argument to that is if the motivation is "I want my Necromancer to command the living dead in battle" well then he/she already does. The actions are just mechanics, and shouldn't spoil your RP.