The Netziv (on the Shi’iltos) notes that most of the Rishonim write that tekiyos d’meyushav were listened to while sitting (hence the name “meyushav”). Yet, the common custom in our shules is to stand for tekiyos. Why, in light of the Rishonim explicitely mentioning to sit, has the minhag changed?
The Netziv cites the chiddush of Tosfos (see last post) that the primary tekiyos were those blown during musaf and explains that sitting was a demonstrative display of the lack of desire to fulfill the mitzvah of tekiyos with the earlier round of blowing. Based on Tosfos' chiddush, the need to avoid a hefsek between rounds of tekiyos is far more pressing, as the bracha on the earlier tekiyos applies to the blowing which will occur much later.
Tosfos' practice exposes one to the risk of being called out of shule for some emergency, for a child who needs attention, for any other need, and missing the latter tekiyos, forfeiting the mitzvah. It also demands a high level of concentration to avoid any hefsek. The reason we stand for tekiyos d'meyushav is not because our standards are higher than those of the Rishonim – quite the opposite. To avoid the danger of something going wrong and missing the latter tekiyos we take the easy route out and stand with concentration to be yotzei while hearing the earlier tekiyos d’meyushav.