When did 'want' stop meaning "in need of"

Not yet.

want

1. have a desire to possess or do (something); wish for. "I want an apple" synonyms: desire, wish for, hope for, aspire to, fancy, care for, like; More

2. (archaic) lack or be short of something desirable or essential. "you shall want for nothing while you are with me" noun

3. (archaic) a lack or deficiency of something. "Victorian houses which are in want of repair" synonyms: lack, absence, nonexistence, unavailability; More

4. a desire for something. "the expression of our wants and desires" synonyms: wish, desire, demand, longing, yearning, fancy, craving, hankering;

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archaic

1. very old or old-fashioned.

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Old doesn't mean dead. Thus, I find the assumption that this meaning has ceased, wanting.

There is a film short written and directed by Keir Black called I Want for Nothing made in 2008 (but not released yet).

Listen to the song "I Want for Nothing," a 2009 effort of the band Wye Oak.

From the 2000 book Texas Anthem by Kerry Newcomb:

I'll be a good husband to you, Rose. And we'll have a wonderful life. You'll be my queen, I promise, and you'll want for nothing.

The historical change may be acoming, but it's not here yet.