1) It's a first level spell that provides free advantage in combat. No action, no concentration, no save.
2) It ruins many other abilities that provide advantage as it is an easy continual source to get it.
3) It creates strangeness in character choices and invalidates others. Warlocks are better off taking Tome Pact and just getting the ritual of Find Familiar than Pact of the Chain. Arcane Trickster and Eldritch Knight subclasses come with a free advantage to an attack once per round, etc.
4) The familiar can't capital-A Attack, and yet it can attack.
5) Why is the enemy (continually) distracted by something that can't attack them? And why is this sort of 'distraction' enough for help? Surely there are many distracting things going on, on the battlefield at any given time. A giant could be fighting 5 PCs all at once and have no problems. Suddenly there is a frog and oh no my guard is down.
6) It changes the familiar from being a nice little creature that can help sometimes in scouting, sending a warning or other message, and such to a major contender in combat. It just feels wrong.
7) Why is the Hobgoblin not attacking the Familiar there? Clearly it is a huge threat which is easily disposed of. Hobgoblins esp. are combat tacticians. It is either distracting enough to be seen as a threat, or it isn't. And if it isn't, then it shouldn't be giving advantage.
This alone shows why it feels bad in play. The creature should be attacking it, but it isn't much fun to have your familiar die all the time, and isn't good cinematically either.
8) Follow up question - Do Gnolls Rampage when they kill the familiar? Why or why not?
I don't think this was the intent at all and it was just ruled this way because the final version of the Help action happened to be written this way. Some things were changed, like the 4 Elements Monk losing their bonus action ability and some were not like Agonizing Blast acting on every blast even though all other abilities like that don't. I think it was a mistake to not just issue errata in the spell or Help action to prevent it. True Strike along with the flavour cantrips are the most underpowered cantrips, but it shows just what the designers thought about giving out advantage.
When someone at the table had a familiar I told them before we started that I wouldn't be allowing any Help shenanigans. The whole table were shocked that was a thing and wouldn't have even thought to suggest it.
My take on these FWIW
Obviously default is that these are subjective to various degree depending on table preferences.
1 "Free" is actually costing with each casting. Also it doesnt grant free advantage in combat. It adds a crearure that might be able to do the help action. Thats different unless table practice decides different.
2 See #1
3 This conclusion on warlocks seems to ignore the chain boon that gives it access to the special familiars which frankly is baffling - that is huge difference for familiar play. If you are referencing the ritual book invoc with tome, consider the longer contact range invoc for chain as well. As for EK and AT, yes, again, see #1.
4 Help is not an attack, but this one i tend to agree with as a general problem with dnd 5e not tied to famiiar that attack is very poorly handled thru the rules. Hits every time you have things like Dragons breath and anything that limits attacks vs actions. Help in,combat can simply be distraction.
5 Things going on on the battlefield are different from things going on to you and coordinated to give one specific ally an opening.
6 Yes it gives the familiar a role in combat *if* the caster wants to risk it. These things are fragile and take an hour to resummon.
7 Honestly, this seems to be the root of all of the above. If the GM decides "familiars wont be attacked" then yep, its too goid for 1st level. That removes the balancing elements from the spell - 1 hr cast, 1 hp, low ac, gone at 0 hp, no death save sequence. See below for a different approach.
8 Familiar is a creature so any effect triggered by zero hp a creature works and the gnoll ability is defined that way. Not sure what the debate here would be.
Back to 7...
In my games its not uncommon fir the mage to keep the familiar out of combat, as much as they can. They know that if they interject it into combat, distracting for key attacks, intelligent enemies will attack it.
This makes them have to weigh "advantage on one attack" vs the 1 hour to recast it vs the value as scout etc for the rest of the time before they can recast.
One magic missile diverted to the familiar kills the standard ones whike still hitting others. Most any AoE kills one. One sorcery point twinning a firebolt likely kills one while still attacking someone else since familiar ac is low. One archer can likely plug it.
This makes inserting it into combat a very risky proposition.
If you as a player dont think its fun to have it killed often, dont send it into combat to be "a major contender", right? You dismiss it when or right before combat and it doesnt get killed. You send it in to become a factor, you got no room to claim no-fun when it gets killed over it (if against savvy opponents)
Unless your gm provides familiar immunity or de facto instant short rest long periods the combat use of the familiar is not anything like free advantage round after round - far from it.