In that case, it could still be managed, depending on how much general waste we have. For example - leaves, weeds, prunings etc. could easily be accommodated in with the general rubbish, in one bin, grass cuttings one a fortnight could go in the other bin. Make sure waste which decomposes is managed for the 2 weekly collection and just put one bin out at a time.
Obviously , people like yourself Muzzy, may have larger families than some of us, but for myself ,it could be managed.
To get back to the original post, I suppose councils have a prerogative to replace any stole bins, so therefore it is their problem if there are any going missing. Pretty annoying for the householder , but easily resolved. Sometimes these bins are simply moved along the road as they do here, when the culprits come out of the Pub