I am having the same problem. Sony bravia blinks three times with Roku plugged in and no image shows up. I unplug it, switch TV off and back on, and then plug Roku in. It works. This is happening all the time.
Sure. I have a Roku Ultra with current software that is plugged into my Sony Bravia fulltime. Occasionally, when I go to power up the TV/Roku the Sony's light is blinking 'Red' and will not power on from either the Roku remote or the TV's remote. Power cycling the Roku or TV has no effect. If I unplug the HDMI cable from the Roku, I can then power up the TV just fine. I then plug the Roku back in and all is well -- for a random period of time from a day or two to a couple weeks. Back in May of 2019 (yes, two years ago) I experienced the same issue and a Roku software update fixed things for a year or so but now it's been back for at least 6 months. I plugged in an Apple TV for a ~month and had no issues.