VAT is a sales tax (or purchase tax). The "value added" bit is a neat scheme allowing tax authorities to collect efficiently - it's nothing to do with value, it's about price; the government taxes transactions (the vendor pays). Like all sales taxes, it's regressive: poor people spend more of their income on purchases than rich people, so they spend more on sales tax.

Income tax and wealth tax are much more progressive, but they're also much harder to assess and collect.

You have to charge your customers the VAT, so if you're employed as a plumber, you actually have to charge the customers directly everything including the VAT. It's not the you who pays it directly, but you have to earn your company the amount including the vat.