That first followup seems patently insane. "We don't know the value of p̂, so we'll assume it's 5/8". Why would you ever assume like that? The Bayesian approach

That first followup seems patently insane. "We don't know the value of p̂, so we'll assume it's 5/8". Why would you ever assume like that? The Bayesian approach appears to me exactly like the Frequentist, without the part where they assume convenient values of unknown parameters.