> There was a time during the Reformation when they were actively burning Bible translations and executing priests who were translating Bibles
First of all, I do not know of many (any?) cases of people being executed for translating a Bible, despite that being a crime at certain points in time. Generally the given reason was for unrepentant heresy -- e.g. someone has pointed out elsewhere that what we know about Wycliffe's trial and inquisition essentially leaves out his translation entirely, focusing instead on the doctrines he espoused. You seem to have the apprehension that there were just dozens of people being thrown on the fires over this, but that's just really not the case. Translation was banned as a blanket measure to control the spread of known heretical translations (e.g. for the Oxford Synod, the Tyndale Bible), it was not a serious concern in and of itself.
> And remind me which language church services in the Latin rite are conducted in to this day?
Do you mean the Roman Rite? There is no such thing as a "Latin Rite". The distinction is important because the language most Roman Catholic services are conducted in is the vernacular one, and has been for 50+ years now. There are a handful of Latin masses (using the old Tridentine missal) still going on, but I think something like 98%+ are using the vernacular missal from Vatican II.
And honestly, even before then... the Latin parts of the Mass were largely prayers which did not change, so you tended to pick them up, especially given that there were parts where you were supposed to speak as well. It's not too hard to memorize what "Et cum spiritu tuo" means. The gospel readings and homilies were themselves in the vernacular, since of course they were longer and meant to communicate teachings to the populace. So I don't understand what your problem is -- fixed prayers being said in vernacular is somehow antithetical to good religion?
But regardless, if you want, today you can go and find a bajillion Catholic Churches doing English mass, or Spanish mass, or Chinese mass, or whatever language you're interested in.