It's literally just fabric.
No fabric is inherently "crass" or "tacky" or "posh" or any of those other things. All those things are just value judgements that we assign to different pieces of fabric according to socio-cultural factors and associations.
There are many things that used to be the preserve only of wealthy upper class people, and as a result those things were perceived as "smart" (or posh, or whatever word you want to use).
Britain's economic landscape has hugely changed over the past 50-100 years, with many aristos who used to be wealthy landowners falling into poverty or relative poverty, and being outshone by the influx of super wealthy Russians and Arabs who have different purchasing patterns. Meanwhile, some of the most profitable UK industries are now those dominated by middle class and working class people, and certain industries (like football, or plumbing) which can be profitable are dominated by people from working class backgrounds and thus perceived as working class.
As a result, the UK now has a class of people who are broadly "wealthy but working class". This, combined with mass production and other economic changes such as the availability of credit, means that for the first time (I don't mean right now, but over the past few decades) working class people are buying expensive or "luxury" items that were once the preserve of upper class or upper middle class people.
Posh people can't stand to see working class people wearing "their" clothing and using "their" products, so those products lost their prestige and their whole cultural association changed.
Burberry is a prime example. Once a posh, fairly dull brand, all it took were a few wealthy working class celebs to adopt it, and their whole reputation was changed. And now upper class people don't want to wear it anymore. The change in brand perception happened very quickly.
Nobody would think logos are "crass" if logos were not so popular amongst working class people. It's that association that makes them crass.
If working class people en-masse started wearing Hermes scarves, or battered old Barbours and whatever brand of welly the Labrador- and Range Rover-set wear, then things would change very quickly.
Funnily enough I was just reading a fascinating anthropology journal article about the same thing happening but with jobs and gender coding, basically the more a job is perceived as female the lower prestige and value it's assigned, and if loads of women start doing a male-coded job it lowers the prestige and value associated with the job.