I think the current rules are a bit funky, so here's some slight changes to how it works.
Whenever possible, find a weapon similar to the object, give those weapon stats when wielded by someone proficient in that weapon. If a person is not proficient in the weapon it's closest to, then they gain the basic stats of an improvised weapon. In either case neither party gains their proficiency bonus, these are not weapons created for and balanced for war. The advantage for being trained in a similar weapon is you have an understanding of how to get the most out of it even if it is wielded awkwardly so you at least get the weapons stats. Otherwise why pay 10 gold for a maul if anyone proficient could just pay 2 gold for a sledge hammer?
If, you have the tavern brawler feat you have learned to wield improvised weapons with proficiency. What this mean is you can provide your proficiency bonus with improvised weapons. However, the damage and traits of a weapon are still limited by your weapon proficiency. Like say, you're only proficient in wielding simple weapons, and decide to use a sledge hammer. Well a sledge hammer is closest to a maul, but a maul is a martial weapon. So the effects are, you may apply your proficiency bonus, but gain basic improvised weapon stats. You're trained in wielding awkward things effectively, but have not mastered it's closest weapon equivalent, so while wielding it efficiently, you aren't wielding it correctly. If, however, you have BOTH proficiency in a similar weapon AND tavern brawler, you could treat that sledge in all ways as if it were a maul.
As an extra bonus:
If you have tool proficiency, you are treated as proficient like a tavern brawler in any tool that falls into that kit, and optionally related tools at the dm's discretion. You use these tools on such a regular basis that even though they are not built for war, it isn't as much an inconvenience to you. You've gotten so used to the objects weight and balance that such is barely noticeable in your hands, and making the switch from weapon to tool is not a hard leap for you. You do not, however, gain the other features of the tavern brawler feat, like the stat bonus, or grapple bonus or unarmed bonus. A carpenter proficient in simple weapons can treat a hammer like the light hammer simple weapon for example.
I think the current rules are a bit funky, so here's some slight changes to how it works.
Whenever possible, find a weapon similar to the object, give those weapon stats when wielded by someone proficient in that weapon. If a person is not proficient in the weapon it's closest to, then they gain the basic stats of an improvised weapon. In either case neither party gains their proficiency bonus, these are not weapons created for and balanced for war. The advantage for being trained in a similar weapon is you have an understanding of how to get the most out of it even if it is wielded awkwardly so you at least get the weapons stats. Otherwise why pay 10 gold for a maul if anyone proficient could just pay 2 gold for a sledge hammer?
If, you have the tavern brawler feat you have learned to wield improvised weapons with proficiency. What this mean is you can provide your proficiency bonus with improvised weapons. However, the damage and traits of a weapon are still limited by your weapon proficiency. Like say, you're only proficient in wielding simple weapons, and decide to use a sledge hammer. Well a sledge hammer is closest to a maul, but a maul is a martial weapon. So the effects are, you may apply your proficiency bonus, but gain basic improvised weapon stats. You're trained in wielding awkward things effectively, but have not mastered it's closest weapon equivalent, so while wielding it efficiently, you aren't wielding it correctly. If, however, you have BOTH proficiency in a similar weapon AND tavern brawler, you could treat that sledge in all ways as if it were a maul.
As an extra bonus:
If you have tool proficiency, you are treated as proficient like a tavern brawler in any tool that falls into that kit, and optionally related tools at the dm's discretion. You use these tools on such a regular basis that even though they are not built for war, it isn't as much an inconvenience to you. You've gotten so used to the objects weight and balance that such is barely noticeable in your hands, and making the switch from weapon to tool is not a hard leap for you. You do not, however, gain the other features of the tavern brawler feat, like the stat bonus, or grapple bonus or unarmed bonus. A carpenter proficient in simple weapons can treat a hammer like the light hammer simple weapon for example.