All Telvanni are going to have spells of flight and teleportation (mark/recall, they probably don't care about the intervention spells though); they don't need a teleporter network. Plus it would seem a bit too much like the Guild Guide network of the Mages Guild, and the Telvanni ought to be a very different take on what it means to be a spellcaster from the Mages Guild.
The masters of the sadrith towers do not need to have a two-way fast travel method to the POB. Either they are on the Parliament and then they have a Mouth here, or they don't and then they have no business here until they do.
They could at most, I suppose, have a one-way teleporter from their own tower to the outskirt of the POB, and rely on Recall for the return trip.
As for what happens to the Mouths when their masters die: it's pretty much irrelevant in vanilla, where they are scripted to simply disappear. E.g., kill Dratha, and Raven Omayn is disabled.
That said, what is the incentive for Telvanni people to
become Mouths? Getting your personality overwritten forever probably would not seem appealing to someone raised in a very individualistic culture. In vanilla (which we're planning on changing), it's supposed to be a step up. By becoming a mouth, you now have a patron and you will eventually get to become a spellwright, reclaiming your independence and giving you the opportunity of keeping up the climb to the ranks of wizard, master, and even eventually magister and archmagister. See some vanilla dialogue for the Mouth topic:
Raven Omayn wrote:There is a Telvanni in Balmora who is ready for the rank of Mouth, but the other Councilors believe that he is not trustworthy. His calls himself Fast Eddie.
Enar Releth wrote:If you are looking for a mouth of your own, you might ask Fast Eddie in Balmora.
Aryon wrote:Each Mouth represents his or her patron, who is one of the older and more respected members of the Council. The Mouths receive messengers from their patrons and cast their patron's votes in the Council.
While other Councilors would insist that you stay in the Telvanni Council Hall day and night awaiting my decisions, I understand the insignificance of the daily business of the Council.
I have heard of a promising Telvanni in Balmora who might agree to be your Mouth, but I do not know more than this. Ask the other Telvanni if they know of someone who would agree to be your Mouth.
You have found a Mouth to represent you on the Council. As your protege, Fast Eddie will do chores for you. I am pleased to see my own protege rise so quickly to the rank of %NextPCRank in House Telvanni. Please accept this glove. It was one of my first successful enchantments.
You have a Mouth to be your voice in the Council.
Edd Theman wrote:You want me to be your Mouth?
Well, I've waited a few years. I can wait a few more.
That's okay. I've been waiting to be a Mouth for years.
If I'm your Mouth, you'll be my patron. You'll need to give me a Silver Staff of Peace.
I've waited for years to be someone's Mouth. I won't disappoint you. I'll go to the Council Hall right away. If you want me to do any chores for you, just let me know.
I said I'd be your Mouth, and I will.
I am your Mouth. Just tell me how you want me to vote in the Council or if you want me to do chores for you.
A possibility is that being a Mouth is not a complete mindwipe and personality rewrite. Instead, it's more like getting a voice in your head. The Mouth keeps their own mind, but there is the copy of the master's mind as well, which gives orders as well. The Mouth's angle is that they hope they'll learn the secrets of their master this way, and will eventually grow their willpower enough to not let their master hold sway on their actions anymore.
Otherwise, all that dialogue about Mouths and Fast Eddie will have to be rewritten. Not necessarily a bad thing, because "Edd 'Fast Eddie' the Man" is a groaner of a name.