As hard to imagine as it may be for more than a few people, IE6 was the best browser of its time. When it was released it had the best support of any browser out there for the web standards of that era. It would be great to see a newer browser that combined modern web compatibility with the simplicity/neat quirks of the classic browsers. Perhaps the closest we've got to that sort of mindset are SeaMonkey & Pale Moon. Opera moved away from Presto, Firefox is turning into a clone of Chrome, and Netscape is sadly long gone. IE5 & IE5.5, its predecessors, are woefully underrated; they are almost identical in web support and more stable. Another nice plus is that those versions, and earlier IE revisions, tend to avoid the web-master's chopping block; sites that block IE6 usually allow them.
I'm with you all the way on this idea--if IE5/6 had HTML5 support and tabbed browsing, but still retained their low memory usage (they work well even on 32MB of RAM), that would perhaps be the ideal browser for me. IE used to be the only browser that would work reliably for me on ancient computers like my IBM Thinkpad 380ED with 48MB of RAM (on which Opera & Firefox ran slow). Turn off SSL 2.0/3.0, enable TLS 1.0, turn off JavaScript/ActiveX and disable all addons/plugins, and IE runs like a true champion.