XLSX files have been around for ... nearly 13-years...
Ugh - I still deal with clients who are creating brand new XLS and DOC files and expecting to have all the latest features (co-authoring when hosted in 365/SharePoint Online/OneDrive/Teams)...
Worked on a world class radiotherapy piece of software. If you like 20 year old Delphi projects and pre C89 ... C, then come over! Xls export is probably a recent addition, xlsx support will most likely come no sooner than when Excel stops supporting xls.
Ten years ago people were still complaining about OOXML not being an open standard. Don't worry guys, I'm sure they'll make a reference implementation of the standard soon! I'm sure there were a few people waiting around for a "real" standard to come out before implementing XLSX support.
I suppose someone had written a VBA macro to import all the CSV files and then save them in a format which could be imported into some dated upstream system. Or never changed how they worked. Could even be because Excel does something slightly more rigorous with XLSX files which made writing the VBA trickier.
I worked with teams integrating legacy systems from hospitals before. There seem to be a large amount of carefully customised scripts for pulling data together. There was never a straight-forward data ETL / export for something other than routinely reported. A lot of information is derived and inferred from even not related (e.g infer chemo events from drug prescription codes if parts of system is not accessible). Hence if you really need high quality data you need a lot of validation and cross-checks as well (either by script or manually). To me it sounds like the checks and validation did not happen enough as the time is very critical. I don't think Excel is the single thing to blame here. Hospital IT systems have a long history of data related issues.
It's also entirely possible that whatever they're importing this data into only supports XLS and not XLSX. I don't think Excel is the ultimate endpoint - the data is getting imported into one or more databases somehow.
e.g. some old versions of Crystal Reports can only do XLS. There must be loads old systems around that can only do XLS