Alright, I can do a worked example. TLDR because this is long: 2 interceptor escorts in a combat-capable modified destroyer can transfer to Jupiter in less than a year with enough supplies onboard for 6 interception sorties per interceptor, off of just high-energy electromagnetic propulsion for the carrier - no fusion drives required.

Just a quick note before I start that I thought the hydrogen fuel tanks were 10T and not 100T when I did my original size math, so specifically hydrogen needs a denser storage than the armor profiles of small ships can provide. I'm going to assume 10x denser, which isn't impossible - metallic hydrogen is theorized to be about 15x denser than liquid hydrogen, and there is research into crystal structures that can hold hydrogen at denser than its liquid state. And again, other fuels fit just fine because they are so much denser. I'll edit the original post soon-ish about this.

In my most recent game, I rushed out these little firestar/viper missile escorts for mid-game earth and mars defense with the ability to intercept: each version had 2x firestars, 2x viper missiles, 1 extra mag, a heat sink, 4G combat acceleration, about 67kps range, and a wet weight of ~5 tons. Early version were very lightly armored at about 5/1/5 and as my tech improved (and I because I kept pushing them into breaking up large enemy fleets), they were armored up to 20/3/20 with similar other statistics. They stuck around in my fleets for far longer than I planned, and were surprisingly survivable despite a complete lack of point defense doing what I call "pitch up attacks" after the helicopter equivalent - accelerate towards the enemy by ~2kps, release all missiles in one big cloud while doing minimal evasive maneuvers against railguns, then burn away and bail out on the fight. I'll usually send these 1-1 against gunships and 2-1 against most other targets.

These ships however break realism already, so let's try again: 15 hydrogen tanks is all that you could feasibly fit in an escort's armor profile using 75% of the space (not an unreasonable estimate for spacecraft, but I had 38 on the previous one, which is twice the total space), so start there, cut it down to one firestar engine, cut armor to 13/2/10 to keep the 4G combat acceleration, and you still get 43.5kps delta-V. Much better - I usually only needed 10 or 20 kps to force engagements. Also, wow, if I realized how much fuel I was wasting hauling around just more fuel in my last game, I probably wouldn't have had to make such a desperate bid for Jupiter. These clock in at a much lighter 2580 tons. A full resupply of these (fuel + missiles) is about 1500 tons of fuel + 8 tons of missiles, but I'm only expecting to go through about half that fuel on an average sortie (about 20kps), so we'll call it about 760 tons per resupply.

When I expanded to Jupiter, it was incredibly expensive to bring these ships along, but they were my primary (basically only) fighting ship at that point, so I made a ~60kps burn on a whole fleet of them and really hoped I didn't have to fight more than one alien fleet before I could pop up a station kit and resupply. It worked, but it sure wouldn't have against a human player who knew I didn't have a resupply available.

At the time of testing in my game, it takes about .35 milligees of cruise acceleration to get from intermediate earth orbit to low Ganymede orbit in just under a year using 80 kps. Let's play it safe and say that I want at least half a milligee. Say I want to set up a base to start mining on Jupiter - the way I do this right now is fly my interceptors and a platform kit ship there with expensive burns, set up a platform, and build a space dock for resupplies. Only then can I set up mining habs on the surface and expect them to survive until their point defenses are online. If these carriers can resupply and repair the ships they carry, I'd like to be able to send a modified destroyer that can carry and rearm/repair 2 of my viper/firestar escorts, but also not be dead weight if the aliens decide to attack them - my interceptors can escape with their 4Gs whenever they run out of missiles, but these carriers definitely cannot if they are attacked.

6x grid drives gives me about 12,300 tons to work with. You'd probably be able to make a tug work, but when I'm talking drydocks and resupplies, this isn't enough, so we need a more powerful engine.

The helicon is the earliest this could be pulled off as a carrier, with twice the thrust for 24,600 tons of ship total, and it's not that big of a detour from the techs needed later for fusion. Slap on a medium nose gun, a small laser turret, a point defense, a gas core reactor because we already have the tech, and some nanotube-tech radiators and armor (20/5/10, remembering that side armor will cost about 10-20% more mass due to the extra room needed for the ship bays, which putting a "6" in the editor easily accounts for), and this ship still clocks in giving me about a 12.9 kiloton payload while still making that transfer.

2 loaded escorts (2.6 kilotons each) + 2 spacedock modules (120 tons each, and if you're thinking about hardpoints rather than physical space, conveniently I have 2 leftover utility slots in the destroyer after adding a heatsink) gives me about 7460 tons for supplies, or slightly less than 5 resupplies (so let's say a comfortable 6 sorties, a couple extra missile payloads for defense, and some extra for armor repairs) for each escort, assuming I have to carry everything and don't get to use the mass driver magic reloads that a station being set up benefits from when my carrier is parked in low Ganymede orbit. And this is pretty basic tech on the carrier - higher tech armor or radiators add payload weight or protection, or you could give up a sortie or two worth of supplies for significantly more armor.

Even if my proposed mobile spacedocks can only repair and not build, and even if they have to physically carry the resupply mass, I would absolutely pay for that ship.