Here is where I stand on multiclassing...I have characters in mind, and usually leveling in a straight class does not fulfill that vision. One of the best things in 5th Edition has been the inclusion of Backgrounds in the character creation process which lets you round out your Skills, Tools, and Languages. This is a step in the right direction for D&D, and I can't wait until the entire "Class" system is dropped for Skills.
One of the interesting things in 5th Edition has been figuring out where the power in a character comes from. An example is the staple of the martial classes, the Extra Attack. This sounds amazing, but as others have pointed out, the SCAG Cantrips scale in such a way that a martial character wielding a 1-handed weapon is about on par with the scaling of the Cantrip. What makes the Extra Attack pull ahead is factoring in Feats like GWM or Sharpshooter. But this is only factoring in straight damage in a white-room scenario. Its why the comment of whether a Fighter 2/Bard 3 is more or less effective than a Fighter 5 is completely impossible to answer. Too much variability exists.
Without question, a player multi-classes a character to gain a wider skillset and to do something they couldn't do as their primary class. The aforementioned F2/Bard3 may be building a specific Skald warrior that is built on the combo of Action Surging several Control Spell if the group got in over its head. In a group where both a Bard 5 and a Fighter 5 exists, maybe this isn't necessary...but the character is still able of Controlling enemies or getting injured allies back on their feet in a way the pure Fighter can't, and capable of getting 2 spells off or wearing armor which the pure Bard can't.
The hybrid sub-classes do a good job of dipping toes into the water, but they are also extremely limiting. I can see why someone may want to Multi-Class to get more of something that the base class isn't providing. For instance, take Arcane Trickster rogues. You get a few spells, but with the restrictions and limitations on spells it might not provide the player with enough, prompting the player to dive fully into the Wizard class to supplement spells and spell slots.
Personally, my character is a Fighter-Battlemaster 5 / Cleric - Light 1. This was not originally optimized, but a way for me to play a "Paladin" without playing a Paladin. The Cleric dip has allowed me to do things I would never have been able to do as a straight Fighter, and the mutli-class experience has enhanced my enjoyment of the game by being able to Cure Wounds, Spare the Dying (saved countless of NPC's this way), and Sacred Flaming. And of course, there is the Divine aspect that can be played up in RP. These are things no level of straight Fighter could compete with.
Speaking of my own personal build mentioned above, I could further Multi-Class to increase my overall effectiveness in other areas. I could take levels in Barbarian so I can tank more effectively (my party is a Wizard, Warlock, and Sorcerer) since I am already wearing magical medium armor. Straight Fighter does not provide anything like a Bear-Barbarian. I could legitimately dip into Paladin for extra Fighting Style (Defense or Dueling), as well as Nova potential via Smites and bonus Healing. I could take some Rogue levels and add Sneak Attack to my damage output since I am already "Shield Slamming" via Shield Mastery to knock enemies prone, which again a straight Fighter leveling would not provide.
So yeah...I suppose the short of it is that I fully support Multi-Classing and building the type of character you want to play. The Hybrid classes sort of scratch that itch, but classes are made up of a variety of abilities that can help create a unique character.
