It is undoubtedly true that many political policies(across the spectrum, or whatever the geometry of your preferred political metaphor is) are incoherent, largely because many individuals' own desires are internally inconsistent and, even where they aren't, they usually have to do some amount of compromising with competing goals in order to actually get something passed into law.
However, elasticity of supply and demand are major factors in considering the policies you mention:
'Sin taxes', on booze, cigs, hookers, etc. are designed to exploit elasticity in two ways: because kids tend to be fairly poor, since their labor force participation and share of capital gains are both low, they usually have very high elasticity of demand; their demand for a good will generally drop sharply, sometimes to zero, with even relatively modest price increases. Here, the 'sin tax' is basically a flavor of Pigouvian taxation, aimed at discouraging voters' children from doing things they don't want them doing. Among adult consumers(especially addicts, what great customers!), demand for sin goods tends to be inelastic, which makes taxing those goods a pragmatic revenue source, since the low elasticity of demand reduces deadweight losses from taxation and means that you won't reduce the number of sales you get to take a cut of by too much in taking your cut. So (while you aren't supposed to say it this cynically in public) 'sin taxes' are actually a pretty sweet deal: they are an easy sell, by tax standards; because they promise to curtail activity that voters dislike(thanks to the high elasticity side of the sin market); but they are also far better at revenue generation than standard Pigouvian taxation, thanks to the low elasticity side of the sin market, who will keep right on buying. It actually works pretty well.
In the case of minimum wage (aside from pure moralizing of the 'living standards below X are unacceptable per se' flavor), the assumption being made(exactly how accurately it is being made is arguable) is that what demand remains for low-skilled workers is actually fairly inelastic(which is less crazy than it might sound, since so much has already been offshored or automated, with the remaining demand mostly coming from people who need warm bodies on site in the US, or idiomatic native English proficiency, or the like); but that the bargaining power of low-skilled workers is approximately fuck-all, since the demand has plummeted from historical highs, and organized labor is nearly dead. If such assumptions are accurate(the second is definitely true, I don't really want to get into an argument about the first, merely to note that it is the assumption being made by those in favor of minimum wage increases), then it should actually be possible to increase the minimum wage without markedly reducing demand for minimum wage workers, since the employers who could make do with fewer(either through robots or China) have mostly already done so. Whether or not it is accurate, it is the operating assumption.
As for 'wage and price controls', I'm not certain what you are referring to. Nixon tried them, back in '71, as a counterinflationary strategy(outcome: unsuccessful) and more far-reaching measures were taking during the world wars; but the various regulations(local, state, national) that are wage or price controls of some flavor are rarely talked about in aggregate like that; and are a giant hodgepodge of various things.