I observe that many coach's websites focus on telling about credentials/themselves on the homepage. What's the advantage and disadvantage of this?

It's a balancing act. You're absolutely right in the observation that the hero is the client, but when a coach tells their own story the reader builds trust. They think, "this person had the same struggle as me and understands what the process is like, therefore I will trust the to relate to my problem and the find a solution." A client also likes knowing that others have trusted you prior to them.

But the website should always be focused on what the client needs because and if they need to hear your story and credentials, that's great. But do have content that asks them about their pain points and the results they're looking for.

People who reach the mentor's website, are looking for advice/counselling in regards to sensitive, private and important issues in their lives. Therefore, the potential clients want to be 100% sure that the mentor has the relevant credentials, experience, skills, beliefs and perhaps a specific methodology to give them what they need. showing credentials does not mean that you shouldn't 'showcase' success stories about clients - although you need to remember that in some cases (and even if the stories are anonymous), the fact that the mentor shares private stories publicly, very well might deter others from opening up and sharing their problems/challenges.
If you take clarity for example, most people review both my profile and my reviews before they decide to use my services, and only after they see that I have the credentials AND that I've successfully helped others, do they schedule a call.
I've successfully helped over 300 entrepreneurs, and I'd be happy to help you. Immediately after scheduling a call, please send me a message with any relevant information so that I can prepare in advance - thus giving you maximum value during the call.
Best of luck

It is completely understandable that coaches focus on their credentials and telling about themselves on the homepage. Potential clients want to have some sense of security.
Yet credentials don't tell the whole story. It is not hard to get credentials. And coaches can say anything about themselves that they want.
On the other hand, many coaches out there have a wealth of experience and learning, but don't have the credentials.
My tip to coaches: encourage an initial, free conversation. Speak about your own personal experiences and how your life experiences relate to what you are coaching.
My tip to clients: contact coaches and speak with them.
be open with them. See if they can answer your questions and speak to your personal needs.
If you want to learn more, contact me!

Tip: Anyone can write anything on a Website.

If you're doing very low dollar coaching, Website content might be a factor.

For high dollar coaching, you may notice some Websites have zero content about anything.

Just an application or opt-in for when site will be open for new clients again.

If you're looking for high dollar clients $1000+/week to month, continuity income clients... it's rare any of these clients will ever come from any Web traffic.

Almost all will come from live talks, direct mail, physical newsletters.

My stats show 80% of my new clients come at or after the 7th contact.

Keep this in mind, Web traffic landing once will tend to be low dollar, high returns, the worst of the worst of clients.

If you're building a 6-7 figure/year coaching practice, you'll have very little focus on Web content.

1.By doing that,its help them to attract client.
2.it help clients to identify what they need easy and etc.