BL had enough problems trying to make their current 4 cylinder meet USA emissions requirements at the time, specially in CA. BL was also in such a finical bind that they simply could not afford an engine certification program for the USA market. The smart thing they did do was the TR8 which was too late to enter the market and once the TR7 established this TR was a problem child in the public, it made little difference in the eyes of potential owners. In time, TR8 became far more desierable than the TR7 that it was based on. In many ways, they are the same car.
While many Triumph purist felt the TR7 / TR8 was not a real Triumph, it really was an improvement over the previous TR3/4/5/6 series cars. Gone was the problem IRS in the TR4A/5/6, tub on frame construction and it's overall dated problem ridden chassis design, improved safety features to meet USA requirements and etc..
What Triumph and BL did do in the USA market was their promotion and marketing. Since they sold something like 80+% of their production in the USA, it was an important market to them. The marketing and good will promoted in the USA via their SCCA racing program is still alive and well today as shown in the "classic sports car market" which is British Car centric.
BMW still owns the Triumph brand name and it is likely they will re-introduce this brand to the USA market similar to the Mini.
While British car folks have a rather amazing and loyal following in the USA, there are far more interesting and better value cars that were built and sold in the USA by the Italians, French and Germans. It just seems car folks in the USA simply don't understand or interested in anything that is not a traditional front engine / rear drive layout on a 1930's vintage chassis.
What is amazing to me is how many designed in problems Brit car owners are willing to put up with. It's like a state of deep denial of what the real problems are and the owners are not willing to admit it and deal with these problems properly. Many of these designed in problems are down right deadly safety problems.