My grandma, a seamstress worked under a fashion designer, attached sleeves in the end as long as I remember. I followed her but modern books show it's done after sewing shoulder then sew the side. I think it's easier too and I changed the way I sew sleeves. So I do same as you do now.

I guess the reason to sew sleeves first independently is to easily work on cuffs without body attached.

Ah ...... now I need a big garden that matches to my shirt! Auf gehts crypto price :D