I will say it, yes, games with trap protagonists are one of my secret pleasures. While there are numerous types of this particular niche in VNs, and there are a disproportionate number of this type of game compared to ten years ago, there are some rules shared by all the greats that I thought I'd put out there.
1. A good trap protagonist is a voiced protagonist. Most trap protagonists are voiced. There are a number of reasons for this, but, regardless of the reason, almost all the 'good' trap protagonist are voiced. There are exceptions (early on) or ones where the voice was added on later (Tsuki ni Yorisou, Otome no Sahou), but they are just that, exceptions.
2. The protagonist has some kind of spectacularly high level skill or attractive point. This really is universal. In some cases it is housework (protagonist in Otome no Sahou) and in others it is physical prowess, force of personality, or artistic talent. However, regardless of what it is, no good trap protagonist is devoid of such skills.
3. There is at least one 'ojousama' heroine. While this is not universal, given the nature of this type of game and the fact that most of the schools they 'sneak into' are girls' schools, this is inevitable. Girls schools, even in Japan, are private institutions, meaning there is inevitably (or so says the kami of eroge) going to be at least one sheltered girl that comes from wealth.
4. There will be at least some drama when the protagonist is 'revealed' to the heroines. Easy transitions make for bad games. All the heroines merely accepting it as if it doesn't matter at all means that there was no weight at all to the protagonist's earlier whini- *coughs* ahem, worrying about being revealed. While this drama might be comedic, tense, or sexual in nature, it should not go without note.
5. At some point, most such protagonists will begin to react naturally as their female persona without realizing it (leading to many fans simply forgetting their original names, such as in the case with Mizuki in Koi no Canvas).
There are two major types of this type of protagonist. One is the 'forceful personality' type, and the other is the 'submissive personality' type. An example of the former would be Ojousama no Hanbun wa Ren'ai de Dekiteimasu, and an example of the latter would be Otome ga Tsumugu Koi no Canvas. In the former case, the protagonist has a clear objective in infiltrating the girls' school, and he uses his personal abilities ruthlessly and aggressively for that purpose. In the latter case, the protagonist loses himself (herself as I sometimes think of Mizuki) in his role so completely that he often catches himself reacting entirely as a female.
I like both types, and I find this particular niche tends to produce a disproportionate amount of good games compared to the rest of the VN world... but then, I'm biased.
Edit: As a side note, for those who are interested in recs involving this kind of thing, there are no truly transgender protagonists in any of these games, as far as I know. There are a few who get addicted to dressing in drag or who live as a woman of their own free will even after the story is over depending on the route (Tsuki ni Yorisou, Otome no Sahou), but as far as I know none of these have been confirmed as actually being transgender. That's not to say that none of the writers/makers have intended any of these protagonists to be such (it is a distinct possibility), but so far, in the games I've played/read, none of them have actually confirmed themselves as being such, even in their own thoughts (though again, some have edged around it or verged upon it).
Edit2: Examples of this type of game that have either a submissive or a dominant protagonist that also are top tier.
Submissive (outside of H, since most H scenes in male-oriented VNs are inevitably bed-yakuza affairs)
Tsuki ni Yorisou, Otome no Sahou
Otome ga Tsumugu Koi no Canvas
Tenshi no Hane o Fumanaide
Ojousama no Hanbun wa Ren'ai de Dekiteimasu
Otoboku (despite appearances, all three games)
Koi Suru Otome to Shugo no Tate (though this one can be borderline at times)
Hmm... there were fewer great ones than I thought... the barrage of endless Ensemble games makes me forget sometimes, lol.