The primary reason this advice is given when dealing with security is that one of the key pillars in making something more secure is by reducing the "attack surface". That is if you remove paths into your system you're reducing your system's overall potential.
When I try to explain why this is so crucial with respect to security I like to use the analogy of a house. If we were thinking of ways to make a house more secure we'd start with things that are obvious. Say the doors and windows. If we do not have a need to build the house with 10 doors, only 2 then it would make sense from a security perspective that the house with only 2 doors is potentially more secure then the house with 10.
The next thing we'd think about is the types of doors and how they're secured. Are they screen doors ore doors made of steel. How they're locked and various other features would go into the considerations of how to make them as well as the entire house "more" secure.
Applying the approach to security
The same things are going on with a system's security. So the removal of unnecessary accounts is just another step in improving a system's overall exposure potential, to being compromised. If these accounts are setup so that they do not allow direct logging in, or if they have 20 character passwords, then their potential has been diminished.
Further still if these accounts have been setup so that they're only allowed to be logged in from a local IP address on the LAN or by applying other methods to lock them down such as only being utilized over SSH, then their risk to being attacked has been reduced such that they're no longer deemed too vulnerable.
Key security concepts
Keep these thoughts in the back of your mind:
- Security is about balancing the tradeoffs of setting up a system so that you can use it in as safe a manner as possible, without jeopardizing the system to being used in manners that you do not wish it to be.
- Security is like layers of an onion. We're trying to add as many as we can to thwart a would be attacker, so that they get tripped up, and give up in trying to compromise our system.
Your other questions
Q1. Do these accounts include process and daemon accounts?
Yes when the advice is given to secure/disable/remove accounts they're talking about both user and system accounts such as the ones used by daemons.
You wouldn't want to leave user accounts on a system for users that no longer need physical access to the system, nor would you want to leave accounts for daemons that have been disabled or have been removed.
Q2. What security problems exist with unnecessary user accounts?
As I described above. These accounts are a potential security risk that an attacker "could" use to gain access. However, their presence, if properly secured, is lowered dramatically.
Q3. Can attackers damage systems with compromised unnecessary accounts?
Only if they're able to gain access to these accounts. If these accounts have been configured so that directly logging into them is disallowed, and there are no daemons/services running under these accounts, then they're effectively very little to no risk from a security perspective.