Technically, you have to use your action to tell your companion to do anything except move. From the PHB, page 93:
On your turn, you can verbally command the beast where to move (no action required by you). You can use your action to verbally command it to take the Attack, Dash, Disengage, Dodge, or Help action.
It says nothing about the animal companion continuing to perform the action you made it do in subsequent rounds. If you want it to keep attacking, you have to keep giving it orders. Effectively, it acts as a surrogate for you in combat. Note that, as pointed out in this answer, the Animal Companion isn't substantially weaker than the Ranger himself, and might actually be stronger, particularly at low levels.
I've seen the houserule that the Animal Companion should continue to attack an enemy once ordered to attack them once suggested quite frequently, and the DM is of course free to decide that this is the case. But this is still a houserule, not RAW.
As for "why wouldn't they just get a guard dog that would do just that after a few months of training", there is currently no explicit option that allows you to do this. You can buy beasts (including a mastiff) that are trained as mounts, but buying/training a dog to attack your enemies (which may include dragons, elementals, ghosts...) is entirely up to the DM. Even if they allow it, such a dog wouldn't get the bonuses that the Animal Companion gets and would therefore be weak at low levels and very quickly become effectively useless.
If all of these animals are active at once, and can all act freely, this is a massive change to the balance of the class.
Due to the benefits of Companion's Bond, a Revised Ranger's animal companion remains competitive in terms of health, AC, and to-hit chance with player character classes, and eventually surpasses them in terms of single-attack damage (because you add your Proficiency Bonus to their +damage modifier).
In essence, you can consider an Attack from an Animal Companion to be roughly analogous to the Ranger making an extra attack, unenhanced by magic...but doing a little more raw damage on hit (before you consider other Ranger's features or spells).
Where this gets well and truly insane is when you pair this with Coordinated Attack (5th level) and Storm of Claws and Fangs (11th level).
For this example, let's consider a Ranger who took nothing but Wolves.
For a 5th level Ranger with this feature, they would have two animal companions. Each companion would attack on their turn, then each would attack again on the Ranger's turn. If the Ranger fights with a bow, this is already as if the Ranger is making 5 attacks per round (6, if dual-wielding instead), with each attack doing roughly equivalent damage to someone with a d8 weapon...considering the boost their damage rolls get from Companion's Bond, balanced by the fact that their stats are slightly lower, so they don't hit quite as often. A bit harder if you keep them close to another melee fighter so the wolves can use Pack Tactics.
Once this progresses up to Level 11, the Ranger now has 3 Companions and is generally making 7 or 8 attacks per round...and now three of those attacks are 5' area AOEs, and with that +4 proficiency boost to their damage, they are now hitting about as hard as someone with a good 2-Handed weapon.
Additionally, if you are increasing AC as their Dex score goes up, by level 12 the Ranger has 3 Wolves with an AC of 20, 65hp, proficiency on every saving throw, and Advantage on every saving throw.
In short, by level 12....you have a character who attacks as often as a max-level Fighter burning Action Surge, most of those attacks hit like a combatant with a 2-hander, and has 195 hp worth of disposable meat shields, with excellent defenses that they can throw into the fray whenever they want (you can rez your animal companion for the pittance of 25gp).
The Revised Beast Master is already a very potent build...giving them multiple Companions would make them devastatingly powerful.
In a word: Yes.
While it may be fairly well-accepted (though debatable) that a Beast Master Ranger is weaker than a Hunter Ranger, allowing the beast to attack freely swings things wildly in the other direction.
For the purposes of demonstration, I'll be using a basic Longbow Ranger, taking the Archery fighting style, starting with 16 dexterity, and taking +2 dex at level 4 and 8 to reach 20 dexterity. I'll be ignoring feats and other ranger builds to keep things simple, but they wouldn't really change the end result much anyways.
I'm using Damage per Round (DpR) as my measuring stick, taking into account chance to hit and chance to crit, using an average enemy AC at each level to get as practical a number as I can.
Basic Longbow Ranger
Wolf Animal Companion:
Longbow Ranger with Colossus Slayer:
Longbow Ranger plus Companion:
As you can see, while things start out OK at low levels, with the Ranger+Beast combo coming out only a bit ahead of the Colossus Slayer, this quickly changes once the Beast gets it's second attack. At this point, the ranger is now competing toe-to-toe with the better Fighter builds for damage potential.
Requiring the Beastmaster to use an action for the initial beast attack helps balance this out a bit, but ultimately it's still very powerful, and probably not wise to allow. As an interaction, it's just straight-up overpowered.