If the ethical case for redistribution rests on the view that (A) inequality is partly the consequence of injustices that need restitution and (B) some people really need the money, and probably deserve it because of A, I can't see why that would leave you favouring a crassly simply form of redistribution like BI over another hypothetical form of welfare system which is better at focusing the redistribution on suffers of injustice and things people really need. That probably wouldn't be identical in design to the current US welfare system, but it wouldn't be difficult to argue that many of the features present in most actual welfare states are better at delivering A and B than a simple monthly transfer of a small amount of income to everybody.

Which leaves us with two main lines of argument against some more traditional form of welfare state. It's "paternalistic", but so are employers when they impose conditions upon people that expect to receive money or expenses from them, and I so don't see anyone making the case that expecting minimum standards of behaviour from people in return for giving them money is in general a bad thing. Secondly, it's expensive to administer, but potentially not as expensive and wasteful as the adverse consequences of an overly-generous basic income (or as deadly as an insufficient basic income). On the whole, better to have lots of subtly wrong things than one big politically-sensitive number that can make or break your economy.

Once you've conceded the case that centralised large-scale distribution is inherently justifiable and worthwhile, saying no to "big government" starts to look more like a slogan than an argument...