The authority boss confirmed his new cabinet team, as well as the chair and vice chair of council committees for the coming year at a full council meeting on Wednesday.
But Councillor Bird said his selection as the chair of the personnel committee had been questioned by a member of his own party.
He said having the leader as chairman of personnel has been in place since 2016 and added it would involve setting the vision for the council and employing senior officers with whom he would have to work.
He also said the chairs of the corporate parenting and health and wellbeing boards are traditionally the cabinet members for those areas.
Councillor Bird, who is also chair of planning, said: “The cabinet is appointed by the leader of the day in accordance with Local Government Act 2000.
“I have taken the opportunity of looking at the diversity of the cabinet along with new members. It’s never easy. The law says, the leader plus nine maximum and you can’t increase that.
“I sincerely hope people will give support to the people who have been appointed to the executive.”
He added: “It has been raised with me as to why the leader is the chair of personnel. That started in 2016 and we have carried it on.
“It is fair to say, it is in line with what is done in Dudley, Sandwell, Wolverhampton and I believe in Birmingham.
“As leader of the council it is within the purview of that leader to have vision over the policy and trajectory of the council going forward.
“It is right and proper for the leader of the council, whoever that might be, to chair that meeting in accordance with that vision.
“Secondly it is right and proper that individual is responsible for interviewing the senior personnel of this council, not least of all a chief executive.
“The leader of the day has to work with that chief executive and then there has to be a rapport between them. I’m glad to say I’ve had that with our current chief executive and the previous ones I’ve worked with.”
“I trust that answers the critics who have raised this with me.”
Walsall Labour group leader Aftab Nawaz said: “I totally agree with Councillor Bird the chair of personnel should be the leader of the council.”