It's been mentioned at least part already, but I would really enjoy seeing these changes:
1. The smite spells do not require concentration.
2. They are cast as a reaction when you hit with an attack.
3. Remove the class ability of divine smite (keep the bonus 1d8 damage at 11).
4. Improve the smite spells a little bit, by making damage the same. Level 1 Smite spell 2d8, Level 2 Smite spell 3d8, etc. They scale upward per spell slot level at +1d8 per slot.
5. Each smite spell has an effect, but still doesn't require concentration. Something set on fire should just keep burning, not require concentration. Continuing effects just keep happening, but allow a save at the end of each turn to end it. The effects also scale per spell slot spent if appropriate. Just for example, make spells like this, with a couple new ones added to keep things interesting!
Level 1
Searing Smite - 2d8 Fire Damage - 2d8 Fire Damage each turn until successful Concentration Save
Thunderous Smite - 2d8 Thunder Damage - Strength Saving Thrown or pushed 10 feet and knocked prone.
Wrathful Smite - 2d8 Psychic Damage - Wisdom Saving Throw or frightened. Wisdom save at end of each turn to end frightened.
Level 2
Branding Smite - 3d8 Radiant Damage - Becomes visible, sheds dim light. Charisma saving throw at end of each turn to end.
Crippling Smite - 3d8 Cold Damage - Dex save or targets speed is reduced to 0. Dex save at the end of each turn to end effect.
Compelling Smite - 3d8 Radiant Damage - Target has disadvantage on any attack rolls not against you. Wisdom save at the end of turn to end effect.
Level 3
Blinding Smite - 4d8 Radiant Damage - Constitution Save or blinded. Constitution save at end of each turn to end blindness.
Dispelling Smite - 4d8 Psychic Damage - End one magical effect or spell on the target.
Draining Smite - 4d8 Necrotic Damage - Gain temporary hit points equal to half the damage dealt.
Level 4
Staggering Smite - 5d8 Psychic Damage - Wisdom save or disadvantage on attacks and ability checks and can't take reactions. Wisdom save at end of each turn to end effect.
Banishing Smite - 5d8 Psychic Damage - Banished to a harmless demiplane. Charisma Save at the end of each turn to return.
Level 5
Destructive Smite - 6d8 Radiant Damage - 6d8 radiant damage to all creatures of your choice within 10' of the target, Dex save for half.
I think the increase in damage for the spells is needed, since you are now restricted to only smiting once per turn and it costs your reaction. Plus, you have to learn the spells. If you don't bother to learn lower level smites, then you can only cast smites at the levels of the smites you do know. I think this strikes a nice balance of improving individual smites, but decreasing the frequency and nova ability.