It might be tough to work out the cost, but we can do some napkin calculations based on the rough numbers we do have.
Koji Fox: On average, the FFXIV localization team usually produces about 250-300 pages of text each patch, and four times that each expansion TGG - July 2018
So about 2250+ pages of text per expansion cycle. A standard screenplay script has about 55 lines of dialogue per page. So assuming the same goes for an MMO script, that would be roughly 124,000 lines of dialogue per expansion cycle. But we also have to keep in mind that there is more than just dialogue included in that number: things like quest text and UI elements are also counted, so the estimate isn't fully accurate.
Another way to think about it would be to go by the total number of hours of voiced cutscenes per expansion:
| Expansion | Voiced cutscene duration (hours) |
|---|---|
| ARR | 8.5 |
| HW | 10.2 |
| SB | 11.8 |
| ShB | 17.9 |
(This doesn't count extra voiced dialogue in encounters such as bosses, solo duties, or trusts.)
The 1 script page to 1 minute of screentime adage doesn't really hold up in reality, but lets use it as a rough comparison given that we're talking purely localized lines of dialogue here. That would work out to about 1,000 pages of dialogue or 55,000 lines of dialogue for just the ShB 5.x voiced MSQ cutscenes. That sounds like a reasonable rough assumption given the other numbers we have. ARR had 82 voice actors across all languages, ShB had over 140.
Endwalker has been said to feature 30% more cutscenes and voice acting, so it seems like it's shaping up to be quite substantial.
Others in this thread have mentioned ESO as a point of comparison. ESO releases about 6,000-8,000 lines of dialogue per chapter (which is roughly once a year):
Morrowind: 6,000 lines of dialogue, "77 actors" (88 credited English voice actors) ESO Live - June 2017
Summerset: 7,224 lines of dialogue, "37 voice actors" (although 95 English voice actors are credited) MassivelyOP - June 2018
Up to Morrowind the game had about 150,000 lines of dialogue in total.
So ESO has many more voice actors in the cast (and many more A-list celebrities) but seems to have fewer lines of dialogue overall to record if our assumptions are right.
As others have said, it mostly comes down to scheduling given that voice acting has to be recorded 9 months in advance and that dialogue has to be locked in well ahead of time. It seems they are getting better at fitting more and more in though.