Come again? Cook's utensils give you 1 extra hit point per hit die, so a total of 2 per day if you have all your hit dice at level 2 (you only regain 50% of your hit dice per long rest, remember.)
The most you can get out of this, then, is <one normal hit die>+2d6+1 (from Song of Rest+Cook's Utensils) +1d6+6 (from Healer), for a grand total of <one normal hit die>+3d6+7 per short rest, or an average of 17.5 bonus HP. Which, to be fair, isn't half bad, though it will burn through Healer's Kits very quickly (using most or all of a kit with every short rest.) That's about a full heal-up each time you spend 1 HD.
However, this is...rather heavily an artifact of being only level 2, where 17.5 HP is a lot. It scales very poorly, however. None of those dice get better until 9th level, when Song of Rest becomes 1d8...which is a mere +1 average healing. The only part that scales at all is Healer, which adds +1 HP per HD of the recipient, so by the time you're level 9, the whole thing is only giving <1 HD>+1d8+2d6+14 = 25.5 HP. By comparison, a middling-Con Fighter (say Con 14) will have grown from ~20 HP to ~76 HP, nearly four times as much HP. Even a lowly low-Con Wizard (say Con 10) will be going from 10 HP to 42 HP. If we considered only level 5, roughly midway between these two points, said Fighter would be at 44 HP (though admittedly the Wizard would only be at 22 HP), while this healing combo would be 3d6+10, aka 20.5 HP on average.
If you know the game isn't going to last much past level 4, this can be potent in Tier 1. After that? Nah, you're really better-served by other things. Sure, it's better than healing potions...but other things you can focus on will give you more bang for your buck. Plus, keep in mind, of these three only Cook's Utensils scales with the number of HD spent. So if you want to get the full benefit, you have to take lots of short rests and only spend one HD each. If you spend more HD at once, you're giving up major benefits, since Song of Rest only gives its basic bonus no matter how many HD you spend, and Healer is only related to short rests because that lets you use it again, it doesn't actually interact with HD expenditure at all.
If you actually manage to get to level 11+, the benefits really aren't worth the time spent anymore. You're restoring less than half of the HP of even a puny weakling Wizard.
At 2nd level song of rest is nice. The healer feat is great. Cooks utensils are minor.
Song of rest does not scale well with only minor improvements. Cooks utensils upscale with levels as the number of hit dice increases. The healer feat also scales up as the hit dice increase, and is better than cooks utensils because it can be used more often and without needing to take place during a short rest.
Song of rest at d6 bonus healing at 2nd level averages 7 hp healing per party member spending 1 HD during 2 short rests (the typical assumption). The bonus from cooking utensils is only 2 hp per day at that level and not much but still a bonus. The healing feat is healing 1d6+6 per (9.5hp) for 28.5 hp healing per party member for 3 uses of a 5 gp 3 lb item. 3 cure wounds spells for 7.5 hp healing in a party of 5 players for 22.5 total obviously doesn't come close to 35 hp from song of rest, 10 hp from cooking, and 142.5 hp from the healer feat.
It's pretty easy for the party to each carry 2 healer kits for 100 uses when they are using 15 a day at that rate. A week's worth of healing supplies isn't a significant cost or encumbrance.
It's not just at low levels anymore, and the time spent is still worth it. Your 11th level example with the same build does little for song of rest which is there regardless of taking the healer feat or not. At that level it's 9 hp healing a day per party member on the same 2 short rests for 45 hp using the same 5 party members. At that point the cooking bonus has gone up to 11 hp per party member and exceeded song of rest for 55 hp (unless the party uses more short rests).
The healer feat is doing 1d6+15 hp healing per use at that point, however, for 18.5 a use. Comparing the amount of hit points to the hit points of the character is misleading because it should be compared to the healing power of spells. Those low level healing spells scale worse because they increase with ASI's spent on the casting ability score. Healing word went from d4+3 to d4+5 if other feats weren't taken. Cure wounds went from d8+3 to d8+5 if other feats weren't taken. A 5th level spell like mass cure wounds with 3d8+5 does the same 18.5 per person with the only advantage being number of actions.
That's also where the significant disadvantage comes in because spell slots used for healing are spell slots not used for something else. The feat is nearly as good as 3 5th level slots on mass cure wounds with the 2 rests in there.
When you question surviving to 11th level with the healing from what I mentioned I would question what healing spells are you thinking are getting the party to that level. The heal spell is good for a nice amount for a single party member but didn't exist for the party until 11th level. Cure spells and healing word spells don't give big individual numbers without a lot of upcasting. Prayer of healing doesn't give big individual numbers and costs concentration and takes longer than the individual actions.
Healing spirit and aura of vitality are the spells that can give higher numbers, still take some time, still take a spell slot that can possibly prevent the damage instead, still requires concentration, and don't actually exist on the bard spell list like heal also does not. Those are slots I might use on suggestion and hypnotic pattern instead and those are spells that force me to drop hypnotic pattern.
At 20th level song of rest is healing 13 hp per day each for 65 hp in that 5 person party. The cooking bonus is 20 hp per day each for 100 hp in that 5 person party. The healer feat is d6+24 (27.5 each use) for 412.5 hp of healing in the day. Could be a 6 person party instead for 78 hp from the song, 120 hp from the cooking bonus, and 495 hp from the feat. Could be a 7 person party for 91 hp from the song, 120 hp from the cooking bonus, and 577.5 hp from the feat. That 7 person party can take a 3rd short rest and it's 136.5 hp from the song, 120 hp for the cooking bonus, and 770 hp from the feat.
TBF, it could also be a small party of 3 people and that changes how effective all 3 abilities are but song of rest and the healer feat can give out massive amounts of hit points spread out over many people.
Taking the healer feat also doesn't prevent a character from taking and casting healing spells either. A big heal can come in handy sometimes. What you should be thinking about is how many spell slots a healer build can save if anyone in the party takes the healer feat, and what those slots will do for the party when they don't need to be used for healing.
The healer feat is very good.