It's not a 'cut-off' and a £200 sub will have considerably better bass performance than the floor standing ones - not to mention far easier to fit in a room
Don't get confused by just reading the numbers
Subs are made to handle bass, and nothing else - floor standing ones have to handle all frequencies.
You will struggle to find a £200 sub to match even the Tannoy V4's mentioned for bass extension let alone one that would have considerably better bass. The BK sub I mentioned earlier is IMO the cheapest sub that has the best frequency response (17hz @-6db) for the money, but it does cost £300. The £200 range subs do seem to be stuck around the 35-38hz region, some are even as high as 50hz, decent bookshelf speakers can easily match this.
Agree, subs are made to handle the LF's, but sticking a £200 sub that has the same or a higher frequency response than the main speaker's is not going to achieve very much, the user would be better off paying more for the main speakers, especially if the sub is going to be bought on a budget.