Exporting Logs in a single file thats not MHT
thats a valid concern you bring up about IE being deprecated. Perhaps you could save the logs in html format (using /ExportSummary) instead, which can be opened by any other modern browser
there is also a zip-ping object in testcomplete called the slpacker. this is a built in object that you can use to zip up whatever files you need : https://support.smartbear.com/testcomplete/docs/reference/program-objects/slpacker/index.html (this would have to be done inside your test scripts, as opposed to the CLI)
typically in a CI environment, there may be a max # of logs kept, in which case TestComplete will generate and store the relevant test logs per build (for jenkins, azure dev ops, etc.) within the temp dir, or within the workspace of the build itself.
if we are trying to keep old test artifacts, then i think you have the right idea about using the CLI arguments of exportlog or exportsummary.