It is very popular in Austrian, in particular the TV series from the 70s with Fritz Muliar as the main actor 1972: https://de.wikipedia.org/wiki/Die_Abenteuer_des_braven_Solda.... The theatre plays are also quite popular. I even read the novel as a kid because my father had it in his library :)
In a nutshell, we did it to ourselves by excessively promoting the novel over the course of many decades.
Starting with the avant-garde movements of the 20's, through the communism era (Hasek was a socialist and a communist) to this day, we've been essentially saying Svejk characterizes the true nature of what it means to be a Czech. You literally hear school teachers tell their students a drunk devious simpleton is considered a role model.
The topic is quite complex, there's more history and politics involved, but I'm not going there.
Disclaimer: By no means am I criticizing the book or people who like it.
I am a Czech as well, and although I know exactly what you are talking about, I have found my own way towards Švejk lately. I am afraid (all of them awesome artists, but too much pushing the novel in the humour direction) Lada, Hrušínský, and Trnka are guilty a lot for the feeling which is prevalent now. Contrary to that, I was fascinated a lot by listening to M.C.Putna’s discussion of Švejk in https://www.mujrozhlas.cz/putnuv-jihocesky-literarni-mistopi... and by listening to the novel in audio, where he understands basically Švejk as “Kafka by other means”, and there is a lot to it.
Švejk is pretty popular in Russia (in some circles, anyway), but FWIW I wouldn't say that the way it is interpreted is as "the true nature of what it means to be a Czech". I think that part is perhaps more for internal consumption?
Why do you think Hasek did you a disservice?