You are correct in saying that the Bible's view of women is obsolete.
However, I do not believe that this will cripple the Bible any more than
the many other obsolescences it contains.
Consider slavery, for example. The Bible contains instructions for slave
owners, and does not say even a single word against it. If anything, it
advocates slavery. Yet, slavery has disappeared from the civilized world
today, and the Bible's viewpoint is cheerily forgotten.
Some churches today, have already abandoned the Bible's view of women
by ordaining them as ministers. So, someday, hopefully, the Bible's archaic
view of women will be as dead as its view of slavery.