I use a good password manager with long, unique, random passwords.
The world is messy, though, and some small fraction of the apps/sites/devices/contexts I need to enter credentials stored in my password manager require manual entry. Some of these are on a device with the password manager, but fail to support auto-fill and block paste. Some of these are on other devices (such as TV streaming boxes). It also applies to every login I need to enter on a new device before my password manager is installed and unlocked.
When I have to enter dozens of high-entropy characters on mobile keyboards, TV remotes, or my sad 3rd-gen MacBook butterfly keyboard, a simple unmasking toggle is a lifesaver. Its absence is a misery/frustration multiplier. I'm not sure how the initial login on an iPhone is, but it took me 4 tries to log in on my newest Android because I had to enter ~40 characters while swapping between the stock alpha/symbol keyboards without an unmask.
I'm sold on the value of using a password manager and aware of the risks of not doing it, so these frictions won't deter me. But I'd be surprised if I'm in the majority, here. I suspect many people will fail into partial or complete non-compliance with the password manager if they regularly encounter these scenarios (or encounter them while the costs of abandoning the effort are still minimal).
I don't think showing the password would actually encourage to re-use a password, but hiding the password may encourage to use a password manager and unique passwords.
1) This needs a [2014] tag.
2) This encourages password re-use and the 2019 guidance really needs to focus on generating unique passwords for each site / property and storing it somewhere secure. The push to move to other forms of security has never been stronger.