"Universalism" seems to be used in different ways, and may not be incompatible with the aim of meeting need. I think there may be an illogical leap in the bit you quote from the article.
Universal social security provided a floor designed to catch anyone who fell on hard times. Welfare was never a luxury.....The fact of universalism gave other layers in society a stake in the social security system.
THEN
Better off families might not have needed child benefit, for example, but it gave them extra spending power they could splash on extra clothes, treats for the children (and treats for themselves). But by extending them a stake, it was hoped opposition to their losing an entitlement would protect those who really needed it.
The leap is from saying what social security was designed for - and the stake everyone had in it (first bit) to a different sort of universality (that everyone should receive benefits).
Does "universal benefit" mean that anyone who needs a benefit will get it, or does it mean that everyone should get it? There may be political advantage in getting a "buy-in" (everyone gets a bit out of the welfare state) but if, as stated, welfare is to provide a floor for anyone who falls on hard times, that's where universality comes in. The state pension may be the only "universal benefit" (paid regardless of income, though taxable) - child benefit only goes to people with children (though may benefit the whole community as an incentive to maintain the population), and no-one is suggesting that disability benefits should go to people who are not disabled. We pay taxes/NI for benefits which we may or may not need in the future (e.g. if we should qualify as disabled) - it's effectively an insurance policy.