Is there any reason to concentrate on the Thunderous Smite spell after using its effects?

Question

There are some spells which you can concentrate on even after they will not provide any benefits, for example the thunderous smite spell states:

The first time you hit with a melee weapon attack during this spell's duration, your weapon rings with thunder that is audible within 300 feet of you, and the attack deals an extra 2d6 thunder damage to the target. Additionally, if the target is a creature, it must succeed on a Strength saving throw or be pushed 10 feet away from you and knocked prone.

Nothing in the spell's description would benefit you should you choose to maintain concentration after having made an attack.

Are there other things outside of the spell's description where this would be helpful? Perhaps there is a feature which grants a buff when concentrating, or one that grants a buff when making a concentration check (Constitution saving throw), or even when making a saving throw in general?

Are there any features or reasons throughout the rules to maintain concentration even after you've hit a creature with thunderous smite?

Answer 1

If you are a War Mage

A wizard of the War Magic tradition gets the Durable Magic feature:

Beginning at 10th level, the magic you channel helps ward off harm. While you maintain concentration on a spell, you have a +2 bonus to AC and all saving throws. (XGtE 60)

You can gain access to both the above and thunderous smite with multiclassing or possibly by using a magic item that lets you cast the spell.

You are under a spell

The target of the spell is the caster. While you maintain concentration there is an active evocation spell effect on you. An observer with detect magic or similar can see this. I have to admit that this is sure to be highly situational. If they are not versed in divine magic, you might be able to convince them that you still get the damage bonus to look fearsome, for example. Or you might be able to feel when you step into an anti-magic zone or similar, because the spell effect will be suspended. Both of these examples are subject to DM rulings, though.

Answer 2

There is no reason for a single classed creature without special items

As you've stated, the are no lingering effects that require concentration. But there is a reason for having the concentration mechanic: you might not hit.

Extending the concentration allows you to still be able to utilize when you do hit a creature.

Please see Szega's answer for a scenario where it applies with either multiclassing or items.