No. There are some religions and cultures that do not believe in organ donation, and there are some people who just cannot stomach the thought of their loved ones being cut apart after death. Their wishes should be respected.
I do think it should be easier for people to indicate their wishes, assuming they have no advanced directive on file. I've lived in a lot of different places, and some of them have allowed organ donation simply by checking a box on your driver's license. I have "I am an organ donor" typed into the In Case of Emergency section of my phone, which can be accessed even if the phone is password protected.
I also think this is a conversation everyone should have with their family. If you wish to be a donor, fill out an advanced directive, and give it to whoever will be the executor of your will, and with your emergency contacts. I have no family left to make these decisions for me, so the last time I had surgery, I had the conversation in the car, on the way to the hospital, with the friend I'd chosen to be my executor. I made my wishes very clear to her, and I trust that she would carry those wishes out if something happened to me.