What you say about "diakonos" is of course true. However, context is important, and the very next verse in 1 Timothy 3 says:
“Let deacons be the husbands of one wife, ruling their children and their own houses well.” (1Ti 3:12 NKJV) (my emphasis).
Quite true. There are various ways of understanding that statement, as follow:
1. Strictly speaking, deacons must be men who are married to one wife. Some would say, that they cannot have been divorced and remarried to one wife, and others would also stress that even if his wife were to pass away he could not remarry, nor could a widower be qualified, even though he had been monogamous.
2. These men must have children living at home. They cannot be married and childless or even having one child. If the children have grown up and left his household, then he is no longer qualified to be a deacon.
3. The wife and children must be faithful Christians who are obedient to their father, who is ruling them well.
4. In addition, all other aspects of the house, such as the duties of servants and slaves must be under the capable management of the deacon.
5. Some would say that verse 12 merely stresses the prohibition of a polygamist for becoming a deacon. The emphasis, then, is on
one wife only. These folks might also eliminate men who have had more than one wife in their life, as in the case of remarried divorcees or widowers. It might also eliminate widowers and bachelors.
6. Verse 11 poses a bit of a stumbling block. Paul could have very simply called the women "wives" rather than "women" to stress that he is addressing the wife of the deacon. In fact, he could have said, "The deacon's wife . . ." Instead it is not definite that the women of verse 11 have any relationship to the man in verse 12. In fact, verse 11 is somewhat redundant, if the wife is included in the household of the deacon in verse 12. Of course it is obvious that the deacon's wife would be under his capable management in verse 12.
7. If the women in verse 11 are not the wife of the deacon in verse 12, but are deaconesses (as some translations have it) then how does verse 12 apply to them? There are several possible answers. The first would be that deaconesses also must be monogamous (perhaps not being remarried divorcees or remarried widows or even widows). Others might say that the verses stand apart from each other, verse 11 applying to deaconesses and verse 12 applying to deacons. Another possibility would be that a man married to a deaconess would still be ruling his household well and his wife would not be usurping his authority.
The bottom line, in my view, is the role of deacons is not clearly spelled out. We know that elders are to oversee the church. Deacons, on the other hand, are merely servants of the church, under the oversight and direction of the elders. They have, biblically, no more authority than a common servant or slave in a household. They simply carry out the work assigned to them by the elders. Whether only men can do that or both men and women can work is open to discussion.
One thing that is not at all in scripture is the idea that deacons are a board of directors in the church corporation with authority to hire and fire professional and non-professional staff members.