A friend mentioned this to me today, on the back of news that they're considering establishing a new one. All I can find is articles stating that the exchange was closed down in 1973 (having merged four separate cities' exchanges a decade or so earlier) but not why, or what happened to its constituent companies (were they just merged straight into the London exchange?).
My friend claims it was due to the anti-Scottish policies of the Westminster government at the time who feared the success of a Scottish economy distinct from the wider UK, buoyed by the North Sea Oil boom - is there any truth to this?
Stock exchanges were once local, because of the physical transaction-- shares had to change hands to clear a trade. So Scotland actually had had four stock exchanges up until 1964 (Glasgow, Dundee, Edinburgh and Aberdeen), when they merged to form the Scottish stock exchange.
In the US, similarly, you could not so long ago find the Baltimore Stock Exchange, the Cincinnati Stock Exchange, the Los Angeles Stock Exchange and so on.
Smaller exchanges had higher costs, and created inefficiencies in pricing, neither buyers nor sellers get good executions when volume is very thin . . . merger or extinction made sense. Consolidation in the UK involved not just the Scottish Stock Exchange, but also other regional UK exchanges-- so it's hard to call it an anti-Scottish impulse-- regional exchanges like those in Manchester and Liverpool also have closed, leaving behind only their fine architecture.
All of these regional stock exchanges were in decline long before their final extinction. Ironically, we now have lots of "exchanges" -- all sorts of trading occuring in dark pools and other digital venues; where it happens is often of importance only for time zone and telecom links. Governance is a second issue-- while stock exchanges don't exert _much_ control over companies, they do exert some. A NYSE listed company is going to be more heavily scrutinized than one listed in Vancouver; companies listed on regional exchanges are looked at with suspicion, often with good cause.
In the US, most shares traded on regional exchanges were "dual listed" -- eg in New York and in their regional market, where they may have had a concentration of shareholders. Such dual listings pose particular arbitrage opportunities, but not much other advantage. I am not clear on whether shares traded on Scottish exchanges were dual listed in London at the time, or solely listed in Scotland-- either case would have been awkward.
Sources:
The Rise and Decline of the UK’s Provincial Stock Markets, 1869-1929
A history of Scotland’s stock exchanges
RECORDS OF THE LIVERPOOL STOCK EXCHANGE
Unifying Regional Stock Exchanges
Dominant and Satellite Markets: A Study of Dually-Traded Securities