pattern - What is a Useful Word™?

_{In the spirit of the What is a Word™/Phrase™ series started by JLee, a special brand of Phrase™ and Word™ puzzles.}

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If a word conforms to a special rule, I call it a Useful Word™.
Use the examples below to find the rule.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ Useful }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ ALL }&\text{ ANY }\\ \hline \text{ NEAR }&\text{ AT }\\ \hline \text{ BORROW }&\text{ BEG }\\ \hline \text{ CURSE }&\text{ BLESS }\\ \hline \text{ SNITCH }&\text{ BLUDGER }\\ \hline \text{ CANER }&\text{ CANNER }\\ \hline \text{ REBS }&\text{ DEBS }\\ \hline \text{ LIGHTEST }&\text{ GRAVEST }\\ \hline \text{ SUPPED }&\text{ LUNCHED }\\ \hline \text{ DIAMOND }&\text{ MOD }\\ \hline \text{ AND }&\text{ NOR }\\ \hline \text{ COVERT }&\text{ OVERT }\\ \hline \text{ QUAYS }&\text{ PIERS }\\ \hline \text{ GREEN }&\text{ RED }\\ \hline \text{ OTHERS }&\text{ SELF }\\ \hline \text{ GAMBLE }&\text{ WAGER }\\ \hline \text{ BLACKEST }&\text{ WHITEST }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

Useful Words™,Not Useful Words™
ALL,ANY
NEAR,AT
BORROW,BEG
CURSE,BLESS
SNITCH,BLUDGER
CANER,CANNER
REBS,DEBS
LIGHTEST,GRAVEST
SUPPED,LUNCHED

DIAMOND,MOD
AND,NOR
COVERT,OVERT
QUAYS,PIERS
GREEN,RED
OTHERS,SELF
GAMBLE,WAGER
BLACKEST,WHITEST

The puzzle satisfies the series' inbuilt assumption, that each word can be tested for whether it is a Useful Word™ without relying on the other words.

These are not the only examples of Useful Words™; many more exist.

What is the special rule these words conform to?

—HINTS—

helpfulness level 0:

The name fits here, technically; a different name might have been more appropriate.

helpfulness level 1:

There are way more Useful Words™ than Not Useful Words™.

helpfulness level 2:

This is likely impossible to solve unless you start with the right words.

Answer

A Not Useful Word™ is a word that...

...can have "one" added somewhere within it to make a new word:

ANY => ANYONE
AT => ATONE
BEG => BEGONE
BLESS => BONELESS
BLUDGER => BLUDGEONER
CANNER => CANNONEER
DEBS => DEBONES
GRAVEST => GRAVESTONE
LUNCHED => LUNCHEONED
MOD => MOONED

NOR => NOONER
OVERT => OVERTONE
PIERS => PIONEERS
RED => REDONE
SELF => ONESELF
WAGER => WAGONEER
WHITEST => WHITESTONE

As for the name Useful Word™...

...Rand al'Thor figured that out in a comment below:

The idea behind the name seems to be based on the downvote tooltip on Stack Exchange. You give minus one for an answer that's not useful, hence "not useful" for a word which, when ONE is 'subtracted', is still meaningful.