R’ Shterbruch in Moadim u’Zmanin answers the Avnei Miluim’s question on mitzvos lav l’henos nitnu (see post here). The Ritva describes the heter to remarry as incidental to chalitzah and the status of tahara as incidental to tevila and not direct hana’ah. However, the case of eiruv is different. The issur of techum is not an extrinsic issur which eiruv happens to lift, but is intrinsically related to the eiruv. The issur techum depends by definition on one’s makom shevisa; eiruv does not lift that issur, but simply moves the makom shevisa so the techum has different boundaries. One might very well say that eiruv is not a matir at all, but is what defines the issur of techum. Therefore, since the hana’ah of moving the techum is a direct attribute of the eiruv, one cannot apply the principle of mitzvos lav l’henos nitnu.
The Rashba and Ran debate whether mitzvos lav l’henos nitnu means simply that the reward for mitzvos is not considered a hana’ah (which is what the Ritva’s question suggested) or whether it means that the physical pleasure that may accompany a mitzvah is also not considered hana’ah. The Ran asks: according to the Rashba’s opinion that mitzvos lav l’henos nitnu applies even when there is actual physical hana’ah, how does one understand the gemara prohibiting tevilah in a cool spring on a hot day (RH 28)? Why in that case is the physical hana'ah a block to performing the mitzvah?