imperatives - Verbs like "go" and "come" which can be followed by another verb directly?

With most English verbs (apart from modals), if you want to put another verb after it, you have either put "to" in front of the verb or use the gerund (if such a construction is even acceptable). For example:

want to eat

like to run / like running

However, for a few verbs, this is not necessary:

Go fetch me some water.

Come eat some food.

Now, they don't necessarily have to be used in commands. For example, you could say

He needs to go fetch me some water.

They should come eat some food.

But in any case, those verbs cannot be used in the ordinary present tense:

*He goes fetch me some water.

*They come eat some food.

The first sentence is jarringly incorrect. The second sentence sounds unusual, albeit not as bad as the first, but it's probably still wrong.

It seems that these verbs can only be followed by another verb directly if the first verb is used in the infinitive or imperative. Can someone give a good linguistic explanation for why this is the case? Is there a name for this phenomenon? Are there any other examples of such verbs besides "come" and "go"?