Make 'other amount' in a Membership Price set be able to specify a Membership Type

Currently only those Price Options created in a Price Set and used for a Membership Dues type of Contribution page can specify a Membership Type. Often our potential members want to join at a Membership Dues amount not listed in a Price Option radio field type. So a useful new feature would be to allow any amount to be used to specify a Membership Type and be recorded as Financial Type of Member Dues.
See
http://civicrm.stackexchange.com/questions/3876/membership-name-your-own-price-above-minimum-on-contribution-page
for one of a number of the requests I have seen over the last few years for such a feature.