Besides wrestling and fencing, why didn´t ancient Western martial arts such as glima, bare-knuckle boxing and the various schools of swordmanship to name a few survive to this day?
Karate, Taekwondo, Muay Thai, Judo and so on are all huge in the West as well as the East, but most of our own older martial arts are sort of obscure and considered eccentric to practice at best. Is it exoticism?
Note that I am note talking about more modern disciplines such as Krav Maga or Sambo.
You may want to search reddit for a Historical European Martial Arts sub to cross-post this to.
I haven't read these threads in their entirety, but /u/wotan_weevil probably answers your question in one of these:
https://old.reddit.com/r/AskHistorians/comments/cpcylz/why_was_everybody_kung_fu_fighting/
It's difficult to say why something didn't happen, but comparing the conditions that commercialized each continent's martial arts should go a long way to describing the discrepancy you observe.
The most popular martial arts in the West are Western martial arts, with boxing the most popular. Boxing, wrestling, and fencing all have active competition circuits, and top participants can take part in high-level competitions including the Olympics. Due to this popularity, and the availability of competition, most people who want to take part in Western martial arts for general sporting or fitness purposes will do mainstream boxing, wrestling, and fencing.
In the USA, boxing has about 6.5 million participants, wrestling perhaps 0.5 million (about 250,000 wrestlers in schools, and USA Wrestling has about 230,000 adult members), and fencing perhaps 0.2 million (the US Fencing Association only has about 30,000 members, but school and casual fencers who don't compete in tournaments appear to greatly outnumber them).
Martial arts other than these have about 3.5 million participants in the USA. About half of them are doing BJJ (Brazilian Jiu Jitsu) and MMA (Mixed Martial Arts); many of these will be doing Muay Thai as part of their MMA. Both BJJ and MMA are modern styles, and both developed in the West. Most of the other half are doing East Asian martial arts, with karate, taekwondo, and judo being the most popular. Karate has about 750,000 participants in the US, taekwondo about 500,000, and judo about 100,000.
None of these data are very reliable (estimates from various sources vary), but the general picture of about 2/3 of US participants doing boxing and wrestling, 1/6 BJJ and MMA, and 1/6 doing East Asian martial arts is a fair estimate. Much of the interest in East Asian martial arts has been media-driven, with the kung fu movie craze of the 1970s driving a lot of early interest, and other movies such as the 1980s ninja movie craze and The Karate Kid (1984) continuing to attract students:
While taekwondo didn't feature strongly in many of these movies, it benefited from good marketing and inclusion in the Olympics from 1980. The New Age movement has furthered interest in taiji (tai chi), but many of these practitioners don't consider themselves as doing martial arts (just qigong).
As for Western martial arts other than boxing, mainstream wrestling, and fencing, they all suffer from competition with these three styles. Regional wrestling styles remain mostly regional, and even exposure in the Olympics (e.g., as a demonstration sport in 1912) and the Nordic Games didn't do much for the popularity of glima. Sword styles other than modern fencing (and to a small extent, military sabre) disappeared as the type of swords and the circumstances of their use evolved - people tended to learn current styles which were important in warfare and duelling (and sport), rather than obsolete styles. Thus, historical Western sword styles were rediscovered (e.g., from manuscript and printed manuals) rather than passed down as living traditions. Savate has survived, and even jogo do pau (Iberian stick fighting), singlestick, and bare-knuckle boxing. Other than savate, kicking has largely disappeared from traditional Western martial arts, largely due to kicks and knee strikes being banned in boxing. Apart from a revival of bare-knuckle boxing as a development from the boxing/MMA scene, student interest in these less popular arts is often driven by an interest in matters historical rather than a desire to take part in sports or compete.