Regarding why it isn’t a two way street – it’s not because Litvishe focus on their own more. In a Litvish yeshiva, i don’t think you’ll find many pictures of any chasidish gedolim. But you will find many types of Litvishe – rav moshe was immensely different from the chazon ish, for instance. They also stress Hungarian gedolei yisroel like rav akiva eiger, the chasam sofer, etc..rav hirsch is mentioned too.
a litvish boy knows about different types of chasidim, and knows about their poskim. They learn avnei nezer, sefas emes on kodshim, eglei tal, and others. You will definitely hear Litvishe rosh yeshivos quote rav tzadok, the shem mishmuel, tanya, kozhnitzer maggid, and others. Not a lot, but you’ll hear it.
For chabad to ignore other chasidim and litvishe would be like a litvishe yeshiva to only talk about rav moshe feinstein all day and no one else, not the chofetz chaim either – just rav moshe.
Chabad boys don’t know who rav vosner, rav menasheh klein, rav chatzkel roth, or tons of other chasidishe gedolei torah vehoraah. They’re being sequestered and cut off from the klal, and it’s sad. It’s also supremacist.
Also, another reason for the rest of klal yisroel ignoring the lubavitcher rebbe was because many gedolim did not hold of him as a legitimate gadol. They ignore rabbi kook as well, and mostly ignore rabbi yoshe ber Soloveitchik for similar reasons. It isn’t common that gedolim argue to the point where one side holds that the other is illegitimate. Rav moshe and the satmar rov had intense disagreements, but they had a lot of mutual respect as well.
The yeshivos wish to exclude rabbinic figures that are themselves controversial.