I would rather ask: why the apostle positively argues that the deacon in particular exercises his office better by having boldness? And, what is it about the eldership that calls for soundness in particular?
I'm not so interested in asking why the term "boldness" is not mentioned in particular when discussing the elder. But see Tit.1:9, where is mentioned his duty to convict the gainsayers.
Recall, the office of deacon is inside the office of elder. If there are no deacons, the duties don't disappear--they come back under the duties of the elders and minister. So, the elders' boldness doesn't just get handed off to the deacons when they're around, thus relieving the former of the need for acts of courage.
Returning to my first question, any office bearer should be among the most exemplary Christians of a given congregation. The deacon will be interacting with people, even Christians, at their worst. He needs to be a man of genuine faith capable of a bold exercise of that faith.
What Paul says in 1Tim 3:13 is that in the proper performance of his duties, the deacon will gain great boldness of faith. And what often follows the quality labors of deacon in the church, is a call unto him to the office of elder; duties of which his prior service has grown him in preparation. I judge that as an elder, he needs more boldness.
I'm not saying every deacon should eventually be an elder. Not every NCO in the military (not many in fact) is bound to be a commissioned officer in due time.
The "soundness" in faith which Paul describes in connection with the elder is tied to his duty to propagate the faith by "sound" or wholesome teaching. Again note Tit.1:9, where the elder should show aptitude for exhorting in "sound doctrine." The deacon does not have the same teaching requirement. That observation doesn't mean he should not be pursuing greater soundness for himself.
