This is beneficial if you are using a public WiFi or an internet connection belonging to a third party. This will not provide the additional privacy that most VPNs provide because you will be the only one using that IP address. This will probably not increase security if you are accessing a website from home via a 'private' VPN, although it would prevent any website from knowing if you are at home or away. If you are using a public WiFi, this will prevent the WiFi host from impersonating any website you try to access, and will prevent the WiFi host from knowing what websites you are accessing.
Yes, this is a reasonable remark. But I am more afraid of unnecessary third-party applications/extensions on my computer and collecting logs about all my visits by VPN provider than the fact that someone will collect information at my one address.
That is one tradeoff of using a VPN instead of using a VPS as a 'private' VPN. You can't really know for sure if a VPN provider is keeping logs.
You don't need any third party application to use a VPN, as you can use an open source application whose code you can inspect to connect to a VPN server. Although if you do this, you may lose some features that many VPN providers offer such as checking the current performance of many of their servers at once and connecting to a specific server accordingly.
Using a VPS as a 'private VPN' may be a good way to achieve "regulatory arbitrage" if you are in an oppressive country and your VPS is located in a country with more protections against searches by government.
And modern systems make a very accurate browser fingerprint. Are you sure that you cannot be precisely identified by it as well as me by one ip?
I am not sure I understand what you are asking here. If you are accessing a website from a specific IP address, and are the only person accessing the website from that IP address, the website will know you are the same person.