Yes, every social choice mechanism has issues, but some have an awful lot more issues than others.
That's actually an invalid use of it; while the concept of "better" is inherently subjective ("democratic" has multiple definitions, but many of them are objective) Arrow's theorem has nothing to do with that one way or the other.
Arrow's theorem says that a certain set of binary criteria that applies to voting systems that map from a set of ranked preferences to a single preference ranking cannot be met simultaneously, but it does not say anything one way or the other about the ability to differentiate objectively among voting systems on continuous-valued axes, including various operationalisations of "democratic".
Some voting systems genuinely are more democratic or better than others in an objective sense. For example, a voting system where one person determined by their status in society has their vote count and everyone elses is discarded is objectively less democractic than a voting system where a ballot is selected at random from all voters and is taken to determine the result.
Neither of these systems is as democratic as a system where everyone votes for their favourite and the one with the most votes wins, and that in turn is not as democratic as a condorcet-loser system, where it's not possible for a candidate that the majority rank last to win.
Just because all of the options have problems, it doesn't mean that there aren't options that are completely dominated by others.
Obviously this is true, but this is rarely one of the voting systems being considered in any discussion about voting systems.
If you think that Arrows theorem really does this, then you should stand by that assertion and defend all voting systems that Arrows theorem applies to as not objectively better than any other voting system that Arrows theorem applies to.
And yes, Arrows theorem applies to Dictatorship/Random Ballot/Plurality/Condorcet-loser methods which are the ones I used in my example.
The general point stands that there is no voting method that dominates every other voting method, but that there can be voting methods that dominate individual other voting methods.