David Bronson suggested to me many times ''Tosphot is always right'' [that is on the outside of the page of the Gemara], and I would have to agree. While on one hand you see a lot of effort to explain the Rambam starting from early Achronim [משנה למלך ]  and that gained a lot of steam from the time of Rav Chaim of Brisk until today, Still it seems this has caused a certain amount of lack of interest and neglect in digging into the depths of Tosphot. I experienced this first hand when I got to the Mir in NY. I had been used to trying to dig into Tosphot, but when I talked to other yeshiva bahurim [students] about  this, they would dismiss this --as irrelevant.  Eventually, I understood the reason for this. They were spending their morning hours  preparing for the classes of the roshei yeshiva [which were along the lines of Rav Chaim of  Brisk. While this is a great and important area of learning, still it leaves that whole area of Tosphot ignored

But even if I would want to recommend a movement of ''Back To Tosphot'', I still would not know how to go about this. The only way I could even begin to see the depths of Tosphot was because I had teachers [in Shar Yashuv] and my learning partner Bronson that showed the way. On my own I could barely manage this except after tremendous efforts. And in the meantime I also have tried to get into the path of Rav Chaim of Brisk as you see in the Avi Ezri of Rav Shach. 

[The basic reasoning here is two fold. One is that the deeper you dig into Tosphot. the more you see he was right all along even though at first glance it does not seem like that. But the Rambam is different, Very often he contradicts the Gemara openly, and it takes a lot of effort to try to fit him back in. And even then it is only a possibility, not a sure thing. For example Nida pg 2. The Gemara holds the teaching about the barrel and the mikve contradict each other. And for that reason it says the teaching about the barrel is R Shimon, not the sages. So for the Rambam to state the law is like both is more than a stretch. It is a direct contradiction. Can one answer this? Yes--but only if one is committed in the first place to say the Rambam must have had some reason for that. But why even start with that? Why not simply go like the Gemara in the first place? Why not be first committed to the idea that the Gemara must have had some reason to say these two teachings contradict?

[I think R. Shimon holds that  חקת השתא  is not a חזקה]=I mean to say this: The Gemara brings the mishna that says if a mikve is found to e lacking the proper amount then everyone who went into it is still not pure. The Gemara then asks from a teaching about a barrel that one put aside to e able to separate truma on it and it was found to be sour. in a public domain all טהרות separated are pure and in a private domain they are a doubt. The Gemara says  the teaching is R Shimon. Though this might be in Tosphot [I forget] I think R Shimon holds   חקת השתא  is not a חזקה so in both cases there is one חזקה against another. The cancel each other and so it is a doubt in case of doubt we learn from Sota. A doubt in a public domain is pure and in a private domain is a doubt. And the sages of the Mishna hold  חקת השתא  is a חזקה so in both cases we  have two חזקות against one and so there is no doubt.  

I think ר' שמעון holds that  חזקת השתא  is not a חזקה. I mean to say this: The גמרא brings the משנה that says if a מקוה is found  lacking the proper amount, then everyone who went into it is still not pure. The גמרא then asks from a teaching about a barrel that one put aside to be able to separate תרומה on it and it was found to be sour. In a רשות הרבים all טהרות separated are טהורות and in a רשות היחיד they are a doubt. The גמרא says  the teaching is ר' שמעון. Though this might be in תוספות  [I forget] I think  ר' שמעון holds   חזקת השתא  is not a חזקה so in both cases there is one חזקה against another. The cancel each other and so it is a doubt in case of doubt we learn from סוטה. A doubt in a רשות הרבים is טהור and in a רשות היחיד is a doubt. And the חכמי  the משנה hold  חקת השתא  is a חזקה so in both cases we  have two חזקות against one and so there is no doubt.  

אני חושב שר' שמעון סבור שחזקת השתא היא לא חזקה. אני מתכוון לומר כך: הגמרא מביא את המשנה שאומר שאם נמצא מקוה חסרה בכמות הראויה אז כל מי שנכנס אליו עדיין לא טהור. אחר כך שואלת הגמרא מהוראה על חבית שהניחו בצד כדי שיוכלו להפריד עליה תרומה ונמצא חמוץ. ברשות הרבים כל הטהרות שנעשו עליו הן טהורות וברשות היחיד הן בספק. הגמרא אומרת שההוראה היא ר' שמעון. למרות שזה יכול להיות בתוספות [אני שוכח] אני חושב שר' שמעון מחזיק חזקת השתא היא לא חזקה ולכן אז בשני המקרים יש חזקה אחת נגד אחרת.והן מבטלות זו את זו ולכן ספק במקרה של ספק אנו למדים מסוטה. ספק ברשות הרבים הוא טהור וברשות היחיד הוא ספק. וחכמי המשנה מחזיקים חזקת השתא היא חזקה ואז בשני המקרים יש לנו שתי חזקות נגד אחת ולכן אין ספק