Alliances need to be forged during times of war. Having Picard, one of the best diplomats in Starfleet, helping during negotiations while simultaneously showing the might of Starleet's engineering prowess could be quite a convincing to potential allies.
I saw a video that talked about it from a different perspective. That Star Fleet having a Sovereign class ship just running around doing various missions meant that you had no idea where this super powerful ship would be. So the Dominion had to prepare for it being anywhere.