Why should a perfectly good equation that describes the evolution of the world (the wave function) go away just because someone made a measurement? To deal with this strange state of affairs, Hugh Everett proposed what would become the Many-Worlds Interpretation in the late 1950s (Bryce Dewitt did a lot of development on the idea, too). The Many-Worlds solution is, in a sense, a platonic one. The mathematical physics stays put, but our notion of what constitutes reality changes. Well, that is an understatement—it really, really changes.
According to the Many-Worlds Interpretation, the wave function is never suspended. Every time a measurement is made, the world splits off into as many copies as there are pieces (terms) in the wave functions. If you are the lab technician making the measurement, you split off into multiple copies, as does the entire universe with you. In each copy, a different value of the measurement is recorded. After the measurement, each copy world goes on evolving and splitting as more quantum events occur.
Sounds wacky, don’t it? Why would anyone believe in a universe that is endlessly splitting into (as far as we know) unobservable slightly-different versions of itself? Here is the point at which, as a physicist or philosopher, your biases will likely show themselves.
People will line up behind the Many-Worlds Interpretation because of its consistency. Its advantage is that it keeps the math whole. There is no special pleading about consciousness intruding on the measurement. There is no sense that our access to the world is limited. You have a beautiful equation. It describes the evolution of physical reality, and that is that.