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Do you mean small in terms of footprint, or small capacity?
The simple answer to both though is that it depends on the club!
The older, rugby-only venues are generally owned by the clubs and have been so for many years. ie since that was the standard size for club grounds. A lot of them also used to have large standing terraces and/or cinder banks (so the capacity was larger than they are now that some of that area has been converted to seating). Those grounds are also usually also in built-up/established areas, and expansion is therefore restricted by surrounding buildings or streets. Redevelopment on a grand scale would not be financially viable so they just update what is already there in most cases.
Clubs that have moved out-of-town will generally have grounds with larger footprints and may share with other sports such as mid-tier soccer clubs or rugby league sides, but again the grounds are usually built to cater for the expected crowd, rather that over-sized to allow for big events.
There is usually more than one stadium in the same town or city, with each sport or soccer team having their own home ground, and bigger stadiums not too far away to cater for larger events, so not the same demand for out-sized capacities.
Venue, Location / Capacity / Rugby Club
Ashton Gate, Bristol / 27,000 / Bristol Rugby (also used by Bristol City FC)
Welford Road, Leicester / 25,849 / Leicester Tigers
Kingsholm, Gloucester / 16,115 /Gloucester
Sandy Park, Exeter / 15,600 / Exeter Chiefs
Franklin's Gardens, Northampton / 15,249 / Northampton Saints
Twickenham Stoop / 14,816 / Harlequins
Recreation Ground, Bath / 14,500 / Bath
AJ Bell Stadium, Salford / 12,000 / Sale Sharks (also used by Salford Red Devils RL)
StoneX Stadium, Barnet / 10,500 / Saracens
Kingston Park, Newcastle / 10,200 / Newcastle Falcons (also used by Newcastle Thunder RL)