And that's the gist of my problem with how you present it: you present the position as Imperial troubleshooter, but it is not. Any imperial troubleshooting will be coincidental to the goals of Heidi, and not the actual goal. It is not position of Imperial troubleshooter, it is a position of Heidi's troubleshooter. Good of Empire may come as a result of it, but it will be a side effect of electoral politics.
And yes, it would put Mathilde in a position where she can, in theory, contest Heidi's ambition if she wants to. But, Heidi is one of few people who are probably better than Mathy at Intrigue, and it'd be playing silly buggers with Heidi on her home turf of court politics. And we cannot really trust Ranald to have our back on this one either. So, odds are, Heidi's agenda will be, within margin of deviation, actual Mathilde's agenda too.
edit: tl;dr: Empire needs a troubleshooter, but a) it has plenty of Greys and some are Lord Magisters, while Dawi have zero; and b) position is not Imperial but Heidi's troubleshooter.