Yes bureaucracy and unfriendly business climate. The VAT things are a mess. The Czech IRS is a ****, they do whatever they want or like. I mean quite likely especially if you are in Prague, you will see no problems. But if you do, prepare for nightmare. It is not wise to depend on survivorship bias.
I can "tax" directly offshore so I have no experience with the UK shell company but I believe it must be simpler than having the Czech company. Bulgaria must be a better option. But this is really hard, I am no expert as well. I am just sure that tax system in any developed country is absolute mess and Czechs on top are just even more unfriendly Germans. Combine it with state servants and you find a den of Vogons. Czech state bureaucrats really can be rude for no reasons, few times I was at the brink of physical confrontation (last time middle aged woman at passport office started to pull my old passport from my hand, because "I must return it to the state", even when in my other hand was clear message from department of foreign affairs that "citizens can hold the expired passport if they wish"... argument that I need that passport to prove for tax reasons that I do not live in that country was not even heard or understood -> R U ready for that?)
As Enzoo or someone like that stated, most likely you will see no problems because they will be happy for some money, but really who knows. Tax officers are not rational, and the last thing they care about is the income for state. Recently the tax authorities completely killed many big companies only because the bureaucrats are incompetent. VAT frauds are a big thing in CZ and you might be suspicious just because you are weird. Everyone with cross border payments is in VAT so that makes everything more complicated (but that is everywhere in EU).
If you talk to God, you are praying; If God talks to you, you have schizophrenia.