Thinking more during the day about vintage free-phase electronic organs, I realized that another factor in the good sound is that the oscillators are not (normally) running continuously, but are triggered for each tone required - and frequently there's a time-constant attached to the speed of build up in volume (the tuned circuits used mean that frequency is, to a large degree, independent of supply voltage, so the keying circuit is pretty simple, as it needs to be given the number of iterations of it in even a fairly small organ. This, of course, adds a further degree of realism as opposed to the instant "on" and "off" that was common in divider organs of the era, electronic switching being a costly option, and difficult to arrange so the the attenuation in the "off" position was low enough.
As to the picture that David posted of organ pipes is very sad - I suppose we should be glad that they're not hiding the speakers of the electronic replacement. That's a practice that, in my opinion, is indefensible, and little short of fraudulent. And even worse when speakers a placed inside old organ cases - sometimes with the installers damaging or destroying good pipework in the process - or where the case is retained simply to house speaker cabinets. It's time the organ world got real about these dubious practices and organ advisers should ban them. (I'm not too happy about the fake "pipe tops" that were part of the case wrok of many reed organs - that's equally false.