I don’t think it’s impossible to be attached to more than one person at the same time. It “may” be impractical depending on the terms of engagements between the parties involved. I don’t think attachment is necessarily the most “important”, I think it’s the mode of love that requires the most commitment, especially long term. It’s also the most costly in the event of a breakup especially within the context of cohabitation.
I answered your question to the best of my understanding.