"I hope this computer work"?

The answer to your question is: because.

More seriously, the subjunctive in English is largely a vestigial organ. There are no particularly hard and fast rules that regulate verb usage or tense in English in the way that a Romance language would require.

In other words, in effect there really is no true subjunctive in English, but rather several ways of approximating it.

If translating the subjunctive from a Romance language to English, instead of trying to make our verbs agree with a mood, we merely change things like word order, the verb itself, etc.

Consider one of the few subjunctive uses in English:

If I were ...

There is very little difference in meaning from:

If I was ...

A Romance language would require that this sentence be conjugated differently. But, English doesn't particularly care.

TL;DR You don't need to use the subjunctive in English because there really isn't one.

Different languages have different verbs that require (with varying degrees of strictness) the use of the subjunctive. In English, we do not generally use the subjunctive with the verb hope. Compare the following, (using the verb to be, as it is more clearly distinguished in the subjunctive):

I hope the computer is working.
I wish the computer were working.

*I hope this computer work.

is ungrammatical (hence the asterisk, which marks ungrammatical sentences) because it is short for

• I hope that this computer works.

which is grammatical.

The that complementizer introducing the tensed object complement clause

• (that) this computer works

is optional, and may be deleted, as in the original example.

But this leaves a tensed clause, in the present tense,
and that means you have to add the 3rd Person Singular Present Tense suffix, -s, to the verb:

• I hope this computer works.

I can imagine that in some languages to hope is connected with a subjunctive clause. But that is no general rule for all languages. English and German don't use a subjunctive after to hope.

Inasmuch as this question can really be answered, we can probably say:

• There is no a priori guarantee that a particular verb will necessarily select a particular structure (be that whether it "takes the subjunctive", how many complements it allows, whether it selects a particular preposition etc), though there may be tendencies.
• The "subjunctive" construction (actually probably more satisfactorily analysed as an infinitive[*]) generally serves to grammaticalise a non-assertion; different verbs are more or less clear cut as to whether what they are introducing is a non-assertion; "hope" is one of the less clear-cut cases, but errs slightly more on the side of "assertion" than "non-assertion"
• The "subjunctive" construction is not the only structure available in English to grammaticalise a non-assertion; we observe that different verbs select different structures, so again, there's little a priori reason to assume that "hope" must select one particular structure
• [Warning: Victorian grammarians may be offended by this next statement- look away now if you're of a nervous disposition...] Of those structures, the English "subjunctive" is probably the least consistently used. It may not even really be a "natural" feature of the language but more of a metalinguistic invention, making it more subject to arbitrary choices and convention.

To give a bit more of an explanation: there are certain clauses that represent archetypal "assertions", i.e. they can be confirmed/negated with a tag, can be reformulated with a 'direct speech' construction. Other cases clearly can't. And some verbs allow both the "assertion" and "non-assertion" variants, depending on a semantic difference.

Assertion:

I insist/suggest that Mary was sacked!

No, she wasn't!

Mary was sacked, I insist/suggest.

Non-assertion:

I insists/suggest that Mary be sacked!

*No, she won't.

Mary be sacked, I insist.

The verb "hope" does not fall completely into either pattern: it allows the 'direct speech' structure, but doesn't allow the "subjunctive" construction.

On the other hand, it's important to understand that the "subjunctive" construction is not the only means that English has for grammaticalising a non-assertion. A (probably more common) means is using an -ing form, e.g. "[Mary being sacked] was disappointing" or using an infinitive, typically with the complementiser "for": "[For Mary to be sacked] was disappointing". The verb "hope (for)" can be used with other structures to lend less assertive force: "I hoped for [all of the computers working] but only one worked".

[*] What we call a "subjunctive" in other languages is generally a conjugated verb, essentially with the similar syntax to any other conjugated verb. The English "subjunctive" is always identical in form to the infinitive and behaves syntactically like an infinitive (e.g. think about how they are negated compared to how "normal" conjugated verb forms are negated).

In terms of common usage we do see "hope" used without the non-subjunctive mood. But if I want to stress that the "hope" isn't very likely, or that I intend to be sarcastic, the subjunctive mood seems to offer a good alternative where I don't need to go all the way to "wish" which suggests a very unlikely scenario.

I originally asserted in some comments here that “to hope” is irregular in that it does not use the subjunctive mood where one would expect it to, “simply because it doesn't”. — I am no longer all too sure of that.

I recently saw an exchange on the internet that went so:

What are your hopes for the 2nd season of Uzaki Chan's anime?

that it not be shit

This usage of the subjunctive mood seemed completely acceptable to me, and reminded me of this discussion. In fact, I find “I hope that the second season not be shit.” acceptable as well, though I would sooner use “won't be shit” instead.

I have the feeling that “hope”, when talking about future, currently uncertain events does govern the subjunctive, but it does not when talking about current events that are true or false.

My own Sprachgefühl certainly finds that:

*I hope he be fine right now.

*I hope the store still be open.

are all objectionable.

However:

I hope he do well on his test tomorrow.

I hope he end up in a good place.

I hope he live a long life.

All don't really seem objectionable to me.

So I would say that “to hope” governs the indicative mood when it express a current event that is true or false and the speaker's hope that it is true, but governs the subjunctive mood when it express a future event, and the speakers hope that it come true.