It works OK for martial combatants, so probably OK for casters
A martial combatant with extra attack can fire a bow, then move, then fire the bow again. This doesn't overpower combat. From this point of view, allowing casters to move between beams would not break anything.
Moving between beams creates "interesting" situations with counterspell
Imagine a warlock, Ára, who can see one foe, Tinco, but is in total cover from a second foe, Parma. Ára casts eldritch blast, sending one beam at Tinco and killing them. Ára then moves out of total cover to attack Parma, at which point in time Parma casts counterspell. What happens?
Does Parma's counterspell retroactively cancel Tinco's death? If not, that depowers counterspell. If it does, then the people at the table have more work as they "undo" damage and other effects. Rewinding time is a hassle.
If you don't allow counterspell at all in this situation, deciding that it must be cast when the mage is first casting the spell, then spellcasters become extremely powerful. Imagine Ára casting fireball while behind concealment (safe from counterspelling) then moving into view and releasing the fireball.
Additionally, is Ára considered to be concentrating during the move? If they take damage while moving (from a reaction attack, for example) do they have to make a concentration save? If it fails, does that change Tinco's death?
These questions need to be answered at the table before the situation comes up at the table.