a HA! I think I found the reason why a lot of Kodomo no Jikan locations are near the Musashiseki station. Asahi Production, the company that animates Kodomo no Jikan is located... "a seven-minute walk from Musashiseki station".
Here's the link,
ASAHI PRODUCTION | Japanese animation company with a high reputation
2-2-10 Sekimachikita, Nerima-ku, Tokyo, 177-0051, Japan
TEL: +81-3-5927-5133
Access
7 minutes walk from the south exit of Musashiseki Sta. (Seibu Shinjuku Line)