No one has any problems with Federation ships being that deep into the Alpha Quadrant. Or the Beta Quadrant. Or the Gamma Quadrant. Or the Delta Quadrant...
Becausde there aren't any Federation ships in 3 of those 4 quaderants.
Let's see...we had the
Excelsior exploring the Beta Quadrant.
We had numerous Federation starships and runabouts exploring and roaming the Gamma Quadrant prior to the Dominion War.
We had two Starfleet ships lost in the Delta Quadrant (albeit they weren't brought there by their own power, they still count as being outside the Alpha Quadrant).
There's nothing onscreen to support any of that.
The Neutral Zone only keeps Federation and Romulan ships from crossing into
each other's territory, but everything else is apparently fair game. The Neutral Zone seems to exist only where Federation and Romulan space collide. Otherwise, Federation ships can freely cross over into the Beta Quadrant--and presumably, Romulan ships into the Alpha Quadrant--as long as they don't violate the other's space.
The peace treaty with the Dominion had no said provision keeping the Federation out of the Gamma Quadrant. It did however, state that hostilities between the Federation and the Dominion were over. Presumably, Federation ships can once again explore the Gamma Quadrant now that the Founders know the Federation never had any intent to invade and enslave them.
Before the annex of Bajor, Federation ships hadn't traveled that far yet either.
That's because they hadn't discovered the wormhole yet. Once they
had a way to the Gamma Quadrant, the Federation didn't waste any time sending ships there.
But this is really neither here nor there, really.
Space is big and three-dimensional, even the "local space" where most of Trek takes place in. There's no reason to think that the Federation is the only nation to send ships into unexplored or alien territory.
They even explained several times on DS9 that they were months away from any Federation outposts or patroling ship.
Who was months away from any Federation outposts or patrolling ship?