The power play is static because the power play formation is optimized. It is built around a superlative talent in Ovechkin, and designed around his generational goal scoring abilities. The efficacy of PP1 has rarely faded when it can establish its formation. The formation has been so pivotal that since it was implemented by Oates/Forsythe, the vast majority of the NHL has switched to some variation of the 1-3-1 formation (where-as before that point, it was only Vancouver and a few other teams using the 1-3-1, while most teams used an overload or umbrella formation). Improvisation shouldn't be required often if all the key personnel are present, as the formation is built around feeding the puck to quality shooters on their forehand for one-time opportunities. Improvisation would largely result in less-than-ideal shooters taking up less-than-ideal shooting locations.
Which player is on the half wall is also not critically important. This power play formation was lethal with Ribiero on the half wall instead of Backstrom, as well. While there's certainly not a huge impetus to shift away from Backstrom, given that he's excelled in that role for years and is one of the league's best pure passers, Kuznetsov should also be able to handle the half wall duties without any substantial issue.
Where the Caps power play has seen dips and surges comes from their zone entries, both in terms of %success and also time to reach their formation.
This article from a few years back covers that. When the Caps PP was at its most lethal, it was not only because they gained the zone successfully, but also because their zone entries allowed them to get into formation very quickly. Some combination of personnel changes and tactical changes have seen that zone entry success erode over the past few years. At this point, a safe bet would be that the swap from Johansson to Kuznetsov does have at least a degree of responsibility in terms of the Capitals decreased ability to gain the zone effectively on the power play.