According to Wikipedia;
The show first started in 1822, and was located at Edinburgh’s Canongate on a site now occupied by the Scottish Parliament. From this point until 1959 the show moved around the towns and cities of Scotland, in one of the RHASS’s eight electoral areas - Perth, Stirling, Strathclyde, Aberdeen, Lothian, Borders, Dumfries & Galloway and Highland. In 1960 the
Ingliston site became the permanent home of the show, opening on 21 June 1960. The move to a permanent location has helped the show develop beyond its original remit, to become a celebration of Scottish food, countryside and its farming.
I know, for example, that the show took place in Peebles during the 19th century when most of the visitors and exhibitors travelled there by rail. This required extensive improvements to the local rail infrastructure.
I agree that it would be easier to relocate the showground than the airport but the price the RHAS were demanding was extortionate. As a result, expansion of the airport will focus on the existing land footprint for the foreseeable future. Now that runway 12/30 has been permanently closed, a lot of development land has been freed up.
The road infrastructure definitely needs to be improved and various schemes have been proposed including new routes to the M8, Newbridge and Gogar but nothing has been approved yet. The proposed new development between the airport and Gogar will require a new road but will bring additional traffic so it's doubtful that congestion will reduce.