why 没出息 becomes useless?
Tl;dr: Your interpreting 息 as 'to cease' is incorrect. 出息 as we know it in modern Chinese is a much derived, figurative meaning.

It is better to parse the word as 沒/出息, i.e. understand 出息 altogether. This is also for the fact that the meaning of 沒 is uncontentious. Also, 息 surely is not a verb meaning 'to cease', because it does not make sense with 出 here. In classical Chinese, 息 can also mean 'breath' (the only definition that fits its glyph origin), or 'profit; proliferation'. That is to say, pay attention to its polysemy, and choose the meaning that makes the most sense.

Let us look at the definitions of 出息 chū xī/xí (息 in first or second tone; mainland Chinese uses the first tone, whereas the second tone is predominantly used in Taiwan) first.


佛教用語。稱呼出的氣息為「出息」。
生產所得的利潤。《喻世明言．卷二．陳御史巧勘金釵鈿》：「梁尚賓聽說，心中又忿，又見價錢相因，有些出息放他不下。」《紅樓夢．第五六回》：「一年在園裡辛苦到頭，這園裡既有出息，也是分內該沾帶些的。」


These are very literal renderings of the word, uncommon and rather archaic: the first entry means 'n. expiration; out-breath' (Sanskrit apāna), which is used specifically in Buddhist contexts. The second entry means 'n. yield; profit (息) from labour/production (出)'. Examples of which are drawn from classics like Dream of the Red Chamber. Note how these correspond to the meaning of 息 in classical Chinese (as listed in point 1.), but none means 'to cease'.

Now let us look at the definitions of 出息 chū xi (息 in neutral tone).


努力向上的趨勢。《老殘遊記二編．第四回》：「把我們的待你好意，都摔到東洋大海裡去，真沒良心！真沒出息！」《文明小史．第三一回》：「從來說三代以下惟恐不好名，能夠好名這人總算還有出息。」
利益、好處。《官場現形記．第二五回》：「現在這兩年，聽說出息比前頭好，所以價錢也就放大了。」
少年男女到了青春期間，體態容貌轉為美好出眾。《紅樓夢．第二七回》：「見智能兒越發長高了，模樣兒越發出息了。」


They mean something like 'prospects; an inclination to persevere and work hard', 'benefit', and 'blooming' (as in one's youth) respectively. The commonest use, however, is the first entry. It appears to be most related to the second non-Buddhist literal definition: we say someone is promising if we think they have the potential to achieve something in life (to produce achievement, so to speak). To contrast polysemy, we drop the tone for the second character when we intend the more colloquial, figurative, and derived meaning.
A word of caution: I believe relating the literal 'profit from labour' to the figurative 'prospects' is the most sensible, but I do not have authoritative evidence. This is however based on the observation that 1) the gain of neutral tone in the second character of compound words usually indicates derivation, and 2) the remaining literal sense of 出息 chū xī/xí is rather limited to Buddhist contexts. Regarding the etymology of 出息 as we mean it today, I found a dubious article that claims it is related to the State of Xi, which I think is too far-fetched.

What is described above is not a unique phenomenon. E.g.: 買賣 mǎi mài means literally 'the collective act of buying and selling'. But 買賣 mǎi mai means figuratively (and somehow colloquially) 'a transaction'. See the first point in my answer to another question here.

So, if you say someone is 有出息, you are commending their effort and regarding them as succeeding in a certain aspect. If you say 沒出息, you mean otherwise. Essentially you think they are unpromising, or good-for-nothing. Perhaps you think they haven't worked hard enough to prove otherwise.


Reference for points 2. and 3.: 教育部重編國語辭典修訂本