You can use the Excel Connector to pull out data directly into Excel. The only option for pulling out a formatted report is the Export Formatted Report option, which exports in XLSX.
XLS is a closed-file format, meaning that developers such as those at Salesforce are not free to generate XLS files legally, and documentation on creating XLS files is intentionally hard to find. This was an intentional design choice by Microsoft.
The "HTML workaround" was the solution that Salesforce came up with to provide something better than CSV to begin with. This is the best that one can do legally to create Excel-compatible files without having a local copy of Microsoft Excel running on a computer and calling its API methods (VB Script, COM API, etc).
The newer XLSX format is well-documented as part of the Open Office Document initiative from Microsoft. This function came out in Summer 18. The current feature preserves the groupings, etc of the report, although comments have noted it is of limited functionality. You'll want to try it out for yourself. Save the report, then access the menu from the Reports list and choose Export.