MM, I think I only did it twice and both times they were slower embryos (morulas I think) that were still growing but a lot slower than the blasty. We definitely had at least one or two embies discarded each cycle that were slower or which had stopped growing. Its always awful which is why we are now big fans of day 2 freeze as we feel in our situation it gives our embryos more of a chance to be transferred and hence a chance at life.
And yes the clinic gave us a chance at them being transferred although we were supposed to have decided on the number of embryos to transfer prior to the cycle even starting and our choice wasn't revisited until the day of transfer. If your clinic is opposed to transferring a slower or degraded embryo I think you can mount a good case (I've know women to have strongly and successfully advocated for their poorer embie while they have their legs up in stirrups!) to give the embie the chance of life. Just know that while you have some rights over your embies (they rarely mention or acknowledge this), there are also guidelines in Australia for Drs to follow regarding multiple transfer and they may still refuse.

They have a responsibility to take the time to discuss these issues with you, although I know in reality there is sometimes a rush on to get all the transfers done and that the FS needs to rush off for another appointment. If you can, try and discuss all these issues the day or so beforehand with the embryologist and FS to have a game plan and a smooth relaxing transfer.

I think a lot of IF couples get bulldozed into doing what the FS/embryologist wants and are working to their timetables and factory line process of IVF (especially in the big clinics) that is prevalent in Australia now. I finally found a smaller more personal clinic that treats each patient with respect and gives you time and a say in what happens to our embies. I believe this was one of the factors in our eventual success.