Parishes are good for finding information from, but usually the person has to know which Parish to look in to get it. They can also help in a large city, like Glasgow for separating people with similar names and dates of birth when looking for their certificates, as can the district subdivisions.
However it has to be noted that parishes can and do straddle county borders, which can confuse some people and lead them to ignoring a correct birth certificate because it was in the wrong parish, when actually it was the correct certificate in the correct parish for that part of the town or village and they weren't aware that the parish straddled two counties.
If I may use an example of Glasgow: it was initially one parish (the burgh of Glasgow), in 1597 the outlying districts of Glasgow became the Barony Parish & after that the burgh of Glasgow was split into four parishes, then the Barony parish was subdivided into eight parishes and so on until the present day.
For general searches using Scotlandspeople as an example when doing a general search, not in the OPR section, after the person's name it looks for County/City next and then the district subdivision of the County/City as a refining factor. Quite often you don't have to choose the parish as the record shows under the county /city section, unless you're searching in the OPR section.
Now most people either know or have a clue as to the city or county for the person they are looking for, but they don't know the parish, or due to the time period the Parish isn't relevant, the exception being the Catholic records where they have missions and parishes.
I think the addition of parishes on profiles is ok, but it would/could overcomplicate the categorization of places such as Old Kilpatrick, the example used earlier in the thread.
I hope this helps and doesn't confuse the issue.
All the best