Just because the HEx takes 2 mintes from starting from its platform at T123 to stopping at its platform at T5, doesn't mean the overall travel time is only up by 2 minutes. Even the Piccadilly Line only has half the number of its trains to T5 compared to the numbers that used to go to T1.
There is no such thing as a train that goes to T1, there is Heathrow Central, and of course the Piccadilly Line has more services there because more passengers use T1,2,3 combined than use T5.
If you get off the train at Heathrow Central, you may have arrived at the relevant station a couple of minutes earlier, but you then have to get over to T1. Alternatively, stay on the train and when you get out at T5, take the lift direct to departures level. Overall there's barely anything in it.
When T5 was designed, there was a choice between the old T1 setup of a separate domestic and international area, or letting domestic pax mix with international to get the full range of airside facilities. BA/BAA went with the latter. Clearly there are going to be pluses and minuses of both - but for an airline like BA with a lot of premium customers even travelling on the domestic routes, having full access to the lounges for all is a major incentive to doing it the T5 way.
T1 has a smaller taxi time to the runways that are the most used, 27L, 27R. So the odd minute gained at T5 can be lost in the 20 minute line of a/c you will be in before take off.
Not really, because BA, especially shorthaul use the intersection departures a lot more than they used to. In addition, on 27s landing aircraft rolling long will have a much shorter taxi to T5 than T1. Even if it were the case that BA aircraft have an average longer taxi time, the fact that their on-time statistics have rocketed since they moved into T5 indicates it hasn't had an adverse effect on overall punctuality.