Is EU roaming supposed to work on any local network or can your home provider restrict your choice to a single operator per country?

From my personal experience while travelling in Western Europe (Czech, France, Germany, Belgium, Netherlands, Austria,Slovakia, Slovenia, Swiss and Italy) if I recall correctly, they all have around 3 or 4 networks in their country but Vodafone is more common among them. I use O2-de, and when I roam I observe that I usually can connect to only one (if the other country also has o2) and can connect to two networks( if the country doesn't have an o2 network). But I could never connect to a Vodafone network with my o2 sim in any country though, only the other options if o2 is not available.

So I assume, if the country has the provider same as yours you are forced to use the same, but if not you may be able to connect to more than one.(in your case Vodafone is present in both DE and CZ)

EU- Regulation only makes the roaming free. To provide you good roaming services it is upto each provider and their agreements with other roaming partners for each country.

For you to roam in a foreign network, your Home operator and the Visited operator must already have a roaming agreement in place (or both have such an agreement with the same roaming hub). So if your operator has agreements with two local operators, you will be able to choose from any one of the two or your SIM will choose one based on its preferred network list (eg. first try A and then B).

What was a commonplace situation is that the Home operator used 'steering'; a technique to force you to register to a specific network (most commonly by rejecting MAP_SendAuthenticationInfo from operator B and allowing it for operator A), however this is limited nowadays.

So what happened most likely in your situation is that Vodafone CZ just didn't have any roaming agreements with other German operators. Same happened for me (Vodafone GR) both in Germany and Ireland last week, Vodafone DE and Vodafone IE respectively.