Tense with 'in the past'

Hello, teachers!

Can we use the present perfect tense and the phrase 'in the past' together? Or should we use the past tense? Which sentence is correct in each group?

1-1. In the past this has often proven difficult.
1-2. In the past this often proved difficult.
2-1. Archaeological sites can be found anywhere where humans have stayed, lived, or worked in the past.
2-2. Archaeological sites can be found anywhere where humans stayed, lived, or worked in the past.

Thank you very much.