Back in the OS X betas, you could've done that and run full-screen BlueBox and had the Finder. Or, run BlueBox in a window, and have the Finder. Back then, they hadn't melded Classic into running side by side, it was still in a window.
Only thing is what's wrong with OS X's Finder?
From the sound of it, Classic uses something on the same level of poor implementation (either due to a feature lacking language or kernel) much like many DOS multitasking systems and even my own threading/multitasking workarounds I have done in the past with good ole Visual Basic for Dos (otherwise known as QBasic).
This is because oldschool crap lacks threading, hell even Windows lacks decent threading. Threading is what UNIX has had for like 20 years and gives it a major edge over everything else. If UNIX wasn't so damn good Apple would have never adopted it .
Actually, Classic is a really, really wierd animal because it's OS 9 running side by side with OS X. Both kernels are loaded and active OS 9 apps draw through QuickDraw, and then the Classic environment displays it via Quartz. In 10.3 and beyond, Classic renders directly to Quartz, supporting window layering and all that jazz. But it still remains that Classic is OS 9, and all the Classic apps run in it. It can still crash, and in older OS X releases that happened... a lot. You'd get the OS 9 system error dialog and then Classic goes away. Or an app would hang 9 and Classic would be hung.
It's a royal work of hackery and a state of the art kludge. It still has to follow its own rules, and uses its own old APIs. Hell, you can even force some Carbon apps to run in Classic rather than using X's native Carbon libs. That's really funky... to have Photoshop 7 running in OS X, then run it again in Classic.
As for your interpretation of the problem, you're exactly right. OS 9 lacks threading. It's a cooperative multitasking system, and uses a completely different API (Mac Toolbox) from OS X (Cocoa and Carbon). Add to that, Apple intentionally designed Classic to be ugly and kludgy in an attempt to force developers to make X native versions of their apps. Well, it worked.