CoherentWeb is a commercial tool designed to do this. Its not an XSLT development tool, its for the batch-testing, publishing and reviewing of XSLT 1.0/2.0 output and is specially suited to XHTML.
This is a .Net tool with a graphical UI and is multi-threaded for performance/resilience. Its totally focussed on input/output and can handle a single HTML file or thousands in a folder hierarchy (like, for a website). It rebuilds your folder structure in a clone, so that all relative links can be tested, there are also watch-variables you can set up to monitor HTML meta-data etc in your output.
You just select a top-level folder, select the XSLT and run. You can quickly review rendered input and output for comparison, selecting an input file automatically shows you the associated output, an XML report summarises all XSLT outputs. Settings are stored so you don't have to repeat things each time you start up the app and want to re-run the XSLT.
This is so different from a typical IDE that its hard to visualise, but there is a YouTube video demo of a website transform if you're interested.