Also, it looks like privacy policy is missing. Even simple non-legalese would be useful; something like this would be ideal:
"I won't pass your email to third parties. I will send you a newsletter but only if you opt in during account setup. You can delete your data at any time."
If I saw a privacy policy written in a way I could understand, I would be WAY more likely to give my money to the premium version of the product.
As long as there was a tiny link (privacy policy for lawyers) with it written the traditional way. I want to know that a company is able to produce a traditional privacy document, but is also smart enough to know I don't want to read one.
Not parent, but for me it is because signing in with my google account is a relatively bigger commitment. They have my email, they can send me marketing content, among others.
On the other hand, I still have no idea what their product does uniquely outside of any todo list. Thus, there is no value for me there outside of the proposal of "Deep Work" which I remember fondly due to the book.
In simple terms, signing in with my account extracts an imagined cost (A company(?) has access to me), and the value presented is not enough for me to justify that cost.
Adding other screenshots, and descriptions of what the application does would allow me to understand what I am getting into, before deciding if it's worth it for me to pay that cost, and thus make an informed decision as to whether I want to sign in or not.
Signing in gives access to user data. In return there should be some utility to the user. If there is no implication of the latter, the user won't give away the former.
It gives access to your name, email and profile picture (if you have one). I don't consider it any different than if the same was asked with a signup form.
Having implemented Google Logins in the past, I always choose that option on sites I see: The site doesn't need to store any kind of password for you. This site also appears to be using the new Google "Cross Account Protection" feature, which will for example automatically log you out of the third party site if you report to Google that your account is compromised.
The product sounds interesting, but I'm not going to link my account unless I can see that the product is legit. i.e testimonials, screenshots, a navigation menu that doesn't just point to home etc..
"I won't pass your email to third parties. I will send you a newsletter but only if you opt in during account setup. You can delete your data at any time."