Grammatical Aspect and Lexical Aspect

As luck would have it, I'm just preparing a talk on aspect at a conference. The problem, with your question is that you're looking at aspect in isolation.

Your sentence (as a sequence of words) is perfectly grammatical. It only becomes ungrammatical (in as much as that means anything) when you put it in context.

1. And what do they do? They build a house next to mine.
2. Before you know it, they build a house next to mine.
3. They build a house next to mine, every year, then tear it down.
4. *They build a house next to mine, right now.

English has no such thing as lexical aspect (verbs that already indicate the completion of the event in their frame) with some exception where the semantics already carries the meaning, such as shop vs. buy.

Verbs such as build, on the other hand are aspect free. This is in contrast to Slavic languages, where most verbs are clearly marked as to aspect. E.g. in Czech, there is no such thing as saying 'shoot (sb) dead'. The verb 'shoot (sb)' already contains the completion (death), whereas a separate verb means 'shot and wounded' (ie. shot without completion).

The reason people's first instinct is to say that They build a house next to mine. is ungrammatical, is that they already assume a default 'generic' context. E.g. last year or right now. This is purely a matter of default frames of reference and collocation. Not grammar.

The way to approach aspect (following Givón), is through the TAM space (tense, aspect, modality). Any utterance is positioning the meaning somewhere in that space. You are never (or almost never) just expressing one of these, you're always also being committed to the other two.

So in sentences 1 and 2, you are talking about a narrative time and negative emotion. It is interesting, how often the 'default' meaning of aspect/tense can be inverted through narration and emotional charge.

Whereas sentence 3 is a simple propositional statement with time and repetition marker which identify the aspectual reading.

In 1-3, the aspectual/modality markers go hand in hand with the tense marking on the verb (plus provide context for its interpretation).

The time/aspect marker in sentence 4, however, clashes with the tense/aspect marking on the verb. And since that is the one likely to be assumed when no such marker is present, the sentence on its own feels 'ungrammatical'.

This has important implications for teaching tense/aspect. It needs to be taught alongside its full communicative function, not just with reference to the timeline and an abstract notion of completion. This is quite often done in modern TEFL materials (e.g. Headway).

I outlined what this looks like in this presentation (it focuses on Czech, but gives the English overview for comparison).