(First I thought it would be very strong and unbalanced, but after the comment of GreySage, I started calculating, and the numbers did not support my assumption)
It is most likely intentional
While I am not aware of any statement from the creators, it is highly unlikely that the follow-up damage was meant to scale, as most 1st and 2nd level spells scale horribly.
Balance
(I will call the proposed change WB+)
I compare WB+ to Phantasmal Killer and Sunbeam, calculating for the first 3 rounds of combat, as encounters usually don't last longer. Concentration is assumed to hold.
Phantasmal Killer (4th level slot)
WB+ positives:
- no save every round
- better damage
- it is easier to start, as Advantage is common
Negatives:
- uses up an action every round
- the enemy can get out of it without a save
- one quarter the range of Phantasmal Killer (bad for Concentration, the target can beat you out of it easier)
Damage comparison
At level 7, when you get 4th level slots, DC 15 is common (8 + 3 proficiency + 4 ability). The expected duration of Phantasmal Killer is 3 rounds against a Goblin (Wis -1) but only 1 round against a Stone Giant (Wis +4). I will calculate with 2 rounds.
The expected monster AC is 15, the spell attack bonus for the same wizard is +7, so the hit chance is 65%.
The full damage with Phantasmal Killer during the 3 rounds is 58.3:
- round: 4d10
- round: 4d10 + 2d10 * 0.65 (PK still lasts, + Fire Bolt)
- round: 2d10 * 0.65 (PK ended, Fire Bolt only)
WB+ is easy, 3 * 0.65 * 4d12 = 50.7.
Sunbeam
WB+ positives:
Negatives:
- the enemy can get out of it without a save
- ends if the target is dead
Damage comparison
At level 11 the DC is 17, I will calculate with 30% Con save chance. So in three rounds against one enemy it is 68.85 = 3 * (6d8 * 0.7 + 27 / 2 * 0.3)
WB+ has the same hit chance as before, the spell attack bonus increases to 9, but the monster AC also grows to 17. It is 3 * 0.65 * 6d12 = 76.05
WB+ looks good at first glance, but if you can get a second target into the area of Sunbeam, it wins easily on damage alone. Add to this the blinding and the ability to use Sunbeam even after the original target is dead.
Other considerations
At higher levels it is much easier to restrain enemies, preventing them to leave the range of Witch Bolt.
At the same time, Magic Resistance and Legendary Saves are more frequent.
Conclusion
It would not be game-breaking to allow the secondary damage to scale. The DMG' definition of overpowered:
If a spell is so good that a caster would want to use it all the time, it might be too powerful for its level
I would definitely not want to use it all the time, even if I had an optimized grappler in my team, and most casters don't.