Adventurers are supposed to be special. In the hands of an adventurer, or their antagonists, proficiency with a longsword is not just the knowledge that you're supposed to put the pointy end in your enemies, but rather that you spent the years mastering the weapon to the point you can actually do so.
Fighters aren't just big dumb louts that spend all their time drinking and gambling and lazing about. They spent years and years, often from the age of children, learning how to use and maintain a wide variety of weapons. Training from dawn until after dark, until your fingers bleed, covered with bruises and with the occasional broken bone from training with practice weapons. That is their legacy, their backbreaking labor to become skilled in the art of war. What was this sorcerer doing with their childhood? Their young adulthood?
Every day spent trying to master their magic so as not to be consumed by it was one not spent running until they vomited while wearing heavy mail, learning how to wear it.
Every day spent attempting to master the creation of convincing illusions was one not spent mastering the bow by learning to lead targets and calculate for wind subconsciously.
Every day spent learning to use charms and smooth talk to get five apples for the price of three was one not spent in swordmanship practice learning to parry an attack and deliver a killing blow.
How did your sorcerer grow up, how did he spend his days? If he mastered the lance and the bow and trained in mail, and now uses these skills along with some magical talents, then he was probably a warrior class first. If he thinks that the spear is a fine way to deal with threats, then he learned it on the line, and in a thousand sparring matches, not sitting under a tree and making glowing lights dance.
Class based systems are hard. And horrible. And if there was a single good way to be rid of them, surely we would be. If you have to, to wrap your mind around it, use multiclassing to simulate your unique character origin and upbringing. A game I played had a good idea: imagine your first three levels as how you began your life, what you experienced, and where you are now.
Did you begin life as a the child of the wild frontiers, learning how to use woodcraft and force of arms to survive the rough wilderness, only to find you had a terrifying magical talent, and now you have decided to focus on nurturing it? Rng1/Sor2. Notice how you don't automagically gain Arcana? You weren't trained in that, you have the skillset you created and built in your life before.
Was your sorcerer a gifted magician from birth, using magic as naturally as your own two hands, and went on to learn to use arms and armors and fight, but has now chosen the life of an adventurer to further their skill with magic and explore the limits of their power. Sor1,Ftr1,Sor2
It goes on and on. If you want a "pure" sorcerer with the fancy capstone, and still want weapons and armor training, a variety of feats exist, this goes the same for other skills and abilities.