Hmm... to look at it another way, let's rank the starter types (best at the top, uncertain/ties share a line):
* Internal diplomacy, stability, getting along with the masters, and so forth
++ Order of Chikai (Good!)
+ Daimyo (pretty good)
- Legions (temperment clash)
-- Courtier (explicitly bad)
* Exernal Diplomacy and maybe trade
++ Courtier (Good!)
+ Order of Chikai / Legions (good with specific groups)
-- Daimyo (explicitly bad)
* Administration and internal development
++ Daimyo (Good!)
? Courter (has probems, but might be able to make it up via trade)
-- Order of Chikai/Legions (both explicitly bad, in different ways)
- War and raw military prowess
++ Legion (Good!)
+ Daimyo (pretty good)
Courtier (meh?)
-- Order of Chikai (explicitly bad)
Basically, daimyo is doing pretty well across the board, other than the diplomacy thing, where she's terrible. The idea here is to go insular for a little while, consolidate, and then start looking for specific, limited diplomatic gains. Accept that this is a slow, rebuilding game - incremental change, rather than dramatic. The daimyo is, honestly, the worst option for dramatic change. The legion has the clash of personalities, and some diplomacy. The courtier has *lots* of diplomacy. The Order of Chikai has some diplomacy in relatively nondisruptive places, but he can also get away with more. A daimyo vote is not looking to change things in dramatic ways.
A daimyo making the same sort of plans would probably come across more threatening simply it's a distinctly atypical move for the Phoenix and demonstrates a little more elaborate scheming. This is undoubtedly not the first time a more militarized clan has used us as their whipping boy, for a daimyo to suddenly break with established Phoenix policy is suspicious, for a military commander fresh off a military defeat? One who is inherently not going to follow traditional Phoenix policy in the first place? It's a lot more self explanatory.
A daimyo doing it is pretty clearly saying "wow. We just got our teeth kicked in, Our military and economic strength is untenable We need to do something about that." The daimyo are all about protection and development, and this obviously feeds into that. Now, the Daimyo *is* going to have more problems with selling this to other clans. In particular, she's not going to know nearly as much about who to approach, or how to approach them, and the military types aren't going to find her as likable, but that's not because the proposition is in any way suspicious.
It's also the case that the daimyo is going to have an easier time selling these ideas back home. With the daimyo's way of dong things, it's expansion, but it's peaceful expansion, and since this depends on the shugenja support, the bit where you're keeping your shugenja happy is important. Also, the daimyo may not get as nice of an agreement int he first place, but she's going to pull it off better overall once the agreements are signed. She has the skill in administration to know where to make changes, and what changes to make to really leverage that shugenja power for economic improvement. A big part of the point here is to get in on marginal land and then make it better, which is something that she's really very good at, and the Legion just isn't.