It might not ever be explicitly stated, but it's apparent through context... Voyager was ill-prepared for a long duration mission, and it wasn't just because they didn't have a full load of torpedoes. The ship just really didn't have the facilities for extended missions. They made it work, but it was clearly a struggle and an unintended role for the ship.
But again, we go back to the original mission profile for VOY when it was launched... and that was to find and retrieve Tuvok and a small Maqui Raider (with the Maqui onboard) in the Badlands.
Given the Maqui were not a 'huge' threat at the time and DS9 was near the Badlands, its likely that VOY just didn't require the resources to do an extended mission beyond those 2 weeks... and it also explains why they only launched with 38 photon torpedoes (though if you ask me I would have launched VOY with a full arsenal).
Any other ship assigned the same mission would have likely been launched with similar parameters as VOY was.
This doesn't say anything really about what mission profiles suited Intrepid classes better, as some crewmembers DID also mention the ship was intended for deep space exploration.... only that the original mission profile for VOY was not deep space exploration (which we know it wasn't) - but this by itself doesn't say the class was never intended for deep space missions (just that the original mission the ship was supposed to last 2 weeks at most).
But given that Intrepid class (or VOY specifically) was able to withstand the conditions in the Badlands better than other ships, it stands to reason this was partially influential in assisting the crew from getting out of hairy situations (like the quantum singularity which trapped the ship, and other stellar phenomena).
Plus, VOY did launch with metaphasic shielding which allowed it to enter a stat's corona and remain there for a while. But this was mostly software based modification to the shields which even the ENT-D was able to implement in TNG before VOY was launched (although perhaps SF integrated this modification on a hw level on the Intrepid class which may have been more efficient?).
Yeah, that much is solidly clear. They're not "just" super old ships. They seem to have received fairly regular upgrades.
This all ties into my Khitomer Accords theory too... that we see so many old, pre-Khitomer Accords type ships was that as part of the arms limitation, the number of ships allowed to be built was reduced. So to keep up the fleet, they couldn't just spam new ships. They could keep what they already had, so they HAD to make them work for as long as possible. I also think there was some provision that in-progress or currently planned ships could still be built for x duration, rather than a hard stop immediately. The probably ramped down production, but still had things rolling out.
I don't think the Khitomer Accords would have negatively impacted SF in that regard.
There was some concern in ST:VI (after Praxis exploded) about SF having to scale down their fleet operations (more like paranoia), but in reality, all that would have meant that SF would have likely repurposed existing ships like the Miranda's which may have been used for border patrols, etc. to do more deep space assignments.
Plus, there were talks about giving Klingons access to a few systems from Federation space.
I also think the Accords put some limitations on R&D and what not, so you end with things like the Stargazer being commissioned fairly late. At the time, they may not have had access to much in the way of new designs, or it could have been something along the lines of new designs needing to go through a review process or some such, which no side would be particularly willing to fast track and it probably took ages to get something approved. So... they just kept building what they had while modifying them as much as possible. I just came up with that part on the fly, but I really like it... Starfleet wants to roll out a new class of vessel. By treaty, they need to submit (limited) specifications to a multi-national review board, who then need to approve the design as being Accords-compliant. Obviously, the Klingons and Romulans would be in no rush to let the Federation build new ships, so the whole process gets held up for along as possible.
I don't think the limitations on R&D would have happened. What more likely happened was a shift in priorities.
Following the Khitomer Accords, there was no need to be on high alert because UFP and the Klingons were actively cooperating with each other. This may have pushed back the launch of the Stargazer because SF may have decided to modify it AFTER it was mostly finalized to adjust to the new mission profile (which would likely be exploration, relief efforts, etc.).
We tend to forget about the Khitomer Accords, but they offer a potential answer for ALOT of issues during this period. There's certainly some odd things that happen, but they can all make sense, given that there was a massive arms limitation treaty recently signed... we also know there was a "Second Khitomer Accords" which may have altered some things and perhaps made it easier to roll out new vessels.
As I mentioned, the K.A. mostly seem to address a shift in priorities. Not necessarily scaling back R&D.
I doubt SF would have discarded new ship designs which may have been more combat oriented and finalized to the point where they don't use them.
Like the 25th century showed us, SF had a number of 23rd century designs which underwent refits to keep them up to date and on par with modern vessels.
Its more likely that SF just delayed their original launch dates and modified them initially while still on the drawing board to make them more suitable for exploration while keeping their combat capabilities?
SF has a point in keeping ships in service for as long as possible - aka if they were originally designed to last 200 years, well, with the eventual invention of energy to matter replicators, construction of various things would have become a lot easier, as would upgrades, maintenance, etc.
In this sense,SF could easily keep a starship which was initially built in the 23rd century, to still be in service in the 31st and beyond... just by that point it would be completely unrecognizeable (and of course assuming it survived for centuries in active service).
Every decade or so, all ships would likely undergo large overhauls and upgrades/refits which would likely include replacing strained frame itself with state of the art one - same material (if SF hadn't changed the underlying material it uses for starship frames) or brand new material and just put it back in the same design - or the design would be adjusted to accommodate newer tech - along with elimination of 'wear and tear' - in essence every large overhaul/refit every 7 to 10 years would have 'refreshed' the ship to basically be 'brand new' - smaller upgrades would follow in between depending on if the ship needs it or not (the Ent-D certainly did after the events of BoBw, along with the Cerritos after its bad experience with the Pakleds - the ship got upgrades which made it able to stand up to the Pakleds a lot better in combat after all).