It may not be convenient, but a second gun is good insurance.
Some good backup guns include (clockwise from top left) SIG Sauer P238, S&W Model 642 (this one has custom grips and sights), a custom-shop NAA Guardian and Ruger LCP.
Should you carry a backup handgun?
If you are a lawman, the answer is almost universally yes and is either formally taught or has been informally strongly suggested to new officers for decades.
A positive response to this question is not so clear for the legally armed, non-sworn citizen, though. Setting aside the inconvenience of having more "iron" on your person, I've observed a strong undercurrent of the perception that if a non-sworn civilian does this and it becomes known among his contemporaries, he's viewed as, at the least, being a bit over the top with his practice of self-defense.
Also, I believe that if he is discovered to be carrying two guns when he has occasion to interact with a police officer, such as being stopped for speeding, he will definitely be dealt with in other than the usual manner.
I have heard others comment--correctly or not--that carrying two guns could be used against someone in court during a self-defense case, believing it would cause that person to be labeled a Rambo, someone who was just looking for an excuse to shoot someone.
Defending carrying two guns with logical and reasonable arguments fails, I think, regardless of the merits, although there are many. Pointing out that lawmen routinely do so and this practice is regularly taught to non-sworn civilians in well-respected self-defense classes gets countered with, "Well, the police face criminals." But I would ask, "Who do we face? Angels?"
Then there's the tactical argument that a second gun is a quicker reload, particularly if your primary gun is a revolver. Now, I agree, odds are you will not need more rounds than what you have in your gun, but do you want to stand around after the fight with an empty or partially empty gun?
Then this: Any gun, being a mechanical device, can fail regardless of how much attention is paid to its maintenance. And it can catastrophically fail at the most inconvenient times. You also might drop or lose control of your primary gun. "Fumble fingers" is not an uncommon occurrence when in a potentially deadly encounter.
You may also have to arm someone else to help control a threat or threats, perhaps while your attention is distracted by calling and speaking to the 911 operator.
I've had need to arm someone with my backup gun on a few occasions. One such was when a fellow agent was in such a hurry to get to a particular assignment he left with an empty holster. On another occasion, an investigator with me found his holstered gun was empty.
A third time was when I stepped into something bigger than I'd anticipated. A fellow off-duty officer who was with me but was unarmed wanted to help and said if I had a spare gun I could give it to him. (Luckily, I did.)
Despite these reasonable arguments for carrying a second gun, I see advocating doing so to a non-believer as a losing battle, for no one can overcome the reality that a good percentage of society looks on gun ownership, carry and use--particularly for self-defense--as acts more offensive than crime itself.
If you do choose to carry a second gun, I recommend picking one that you or anyone else can fire without any more instruction past "Point and pull the trigger. Repeat until empty." The gun should also be carried so you can use it with either hand. If this is not practical, carry it to favor off-hand use.
I also have to admit that as I've become semi-retired, my world is mostly home office, range, FFL dealer for gun transfers and gossip, as well as quick trips to the store and back. More often than not, these days I'm carrying only an S&W Model 42 five-shot two-inch revolver for the same reasons others do--it's just so convenient.
But I'm getting over it. After all, who would want "It was just so convenient" as his or her epitaph?