@ Logos
Well most resident on-access AVs as far as I'm aware also have on-demand scanning, so I'm not so sure you would come across that scenario too often other than perhaps cloud AV solutions.
I think avast's full range of shields (web, p2p, IM, mail, etc.) to try and keep malware out, backed up by the file system shield (FSS) much depreciates the need for an on-demand scan. For the most part on-demand scans are going to be scanning what are dormant or inert files, the FSS would be scanning active files.
However, new signatures are added constantly and generic/heuristic signatures updated, so it is possible that something that was previously undetected could be picked on the on-demand scan (depending on the scan type). Whilst active files should be picked up by the FSS on-access scanner.
I too never bothered with scheduled scans with avast 4.8 Home (using the ashQuick.exe hack); as you mentioned the convenience of the avastUI and inclusion of scheduled scanning even in the free version, I do a scheduled weekly Quick and monthly Full System scan.
Since I'm using avast I don't have to make the decision about an AV that doesn't have on-demand scanning, so that bridge remains uncrossed.