This answer is build from Tosfot in Nazir 57a (see also the Tosfot in Chulin 9b and Tosfot Nidda 2a).
But now the Gemara learns a leniency - As a Sotah happens only in a private domain, so too does this rule apply only in a private domains.
Why? Let's say there's no extra stringency of Sotah. Why doesn't it fall back to the old classical "Safek DeOraisa Lechumra"?
First, you seem to assume that this rule of safek deorayta lachumra is a rule deorayta, it is not obvious.
Anyway according to Tosfot in Nazir there is a simple answer to Why doesn't it fall back to the old classical "Safek DeOraisa Lechumra"?
I assume that you ask for sota in public domain. You will see below that no particular leniency is learned from sota according to Rabanan and that safek deorayta lechumra is not said when there is Chezkat tahara.
Here is a stuff from this Tosfot:
באומר ראיתי שנזרקה טומאה ביניכם. והוא עומד מרחוק דהוי ספק טומאה ברשות היחיד ואם תאמר אם כן יביא כל אחד קרבן טומאה ודאי דכל ספק טומאה ברשות היחיד שורפין עליה [תרומה] ויש לומר דלא גמירי מסוטה אלא דבר שאפשר להיות כסוטה דאפשר שנטמאת אבל הכא לא אפשר לטמאות שניהם דודאי אחד טהור
One of two nezirim became unclean, they were alone, in a private domain. Despite that the din of doubt about uncleanness in a private domain should apply for each of them, since we know that only one of them is unclean, and we learn from Sota only a possible interpretation of the doubt, each Nazir is safek unclean and cannot make offer a Korban Tum'a.
ואם תאמר אם כן מאי פריך מעיקרא והא ספק טומאה ברשות הרבים הוא כלומר ויביאו שניהם קרבן טהרה והא ספק טומאה ברשות הרבים דמטהרינן נמי מסוטה גמרינן לה ולא ילפינן אלא דבר שאפשר להיות והכא בודאי אחד טמא
If it's clear for the Gemara that we learn from Sota with a restriction, so in public domain too, they cannot be regarded as both clean, because we know that one of them is unclean.
ויש לומר דספק טומאה ברשות הרבים לאו מסוטה גמרינן ליה
Tosfot explains that the novelty learned from Sota is the din of safek tum'a in private domain, not the din in public domain. {this is congruent with the opinion of Rabanan in Nidda 3a, following which the chiddush of Sota is the Vaday tame in case of safek. In reshut harabim, case sota shenistera is not a safek}
אלא כל חד וחד מוקמינן אחזקתיה וילפינן ליה מקרא פרק קמא דחולין (דף י:) להעמיד כל דבר אחזקתיה** אף על גב דודאי אחד טמא כיון דלא ידעינן ליה
In public domain, the safek nezirim treatment doe's not result from Parshat Sota, each of both nezirim benefits from his chezkat tahara.
ואף על גב דבפרק קמא דחולין (דף ט' עמוד ב') למאי דקא סלקא דעתיה קאמר התם הילכתא גמירי לה ומשמע התם דספק טומאה ברשות הרבים לאו משום חזקה אלא נגמר מסוטה
There is a Gemara in Chulin 9b which states that safek tum'a birshut harabim tahor when we have chezkst tahara is learned from Sota.
במסקנא לא קאי הכי ובמקום אחר [בריש מסכת נדה.] מפורש באורך:
This Gemara in Chulin doesn't follow the conclusion of suggia for the opinion of Rabanan. But for Rabbi Shim'on, this is the final rule, to learn from sota in public domain for a safek without chezkat tahara, because Rabbi Shim'on regards the chezkat tahara of the sota as cancelled.
The point that addresses your question is that Safek Tum'a in private domain is the "natural case of safek", which can be influenced by the Chezkat tahara. (this din doesn't result from halachot Sota according to rabanan).
The Gemara does not learn any leniency from Sota in reshut harabbim. The leniency is generated by the Chezkat tahara.
In masechet nidda at the first two dapim, there is a discussion between Rabbi Shim'on and Rabanan regarding the learning from Sota. Sota has objectively two features.
- There is a great reason to be suspicious because she did wish to be with this man against the prohibition of her husband {raglayim laddavar} so this is a little worst than a simple case of doubt.
- A second feature is that in the presence of someone else man and woman would probably not do nothing {this gives a special reason to see the safek sota in public domain with a special leniency}.
One of the two features would restrict the comparison between Sota and different cases of doubt. For Rabanan the leniency of Sota in public domain is not comparable to other doubts, and is not a source of learning. In the footnote of my second answer, you can see that this principle for rabanan is less clearly explained in other sugiot out of masechet nidda, but the Talmud is congruent with itself and the public domain for sota is a paradigm of safek + chezkat tahara.