CapnZapp
Legend
The first paragraph (lines 1-5) define the concept of "improvised weapons".PHBp147-148 said:Improvised weapons
Sometimes characters don’t have their weapons and
have to attack with whatever is close at hand. An
improvised weapon includes any object you can wield
in one or two hands, such as broken glass, a table leg, a
frying pan, a w agon wheel, or a dead goblin.
In many cases, an improvised w eapon is similar
to an actual weapon and can be treated as such. For
example, a table leg is akin to a club. At the DM’s option,
a character proficient with a weapon can use a similar
object as if it w ere that weapon and use his or her
proficiency bonus.
An object that bears no resemblance to a weapon
deals 1d4 damage (the DM assigns a damage type
appropriate to the object). If a character uses a ranged
weapon to make a melee attack, or throws a melee
weapon that does not have the thrown property, it also
deals 1d4 damage. An improvised thrown w eapon has a
normal range o f 20 feet and a long range o f 60 feet.
The next two sentences tell DMs they can use existing weapon stats for some improvised weapons. The example given is "use the club stats when somebody swings a table leg".
The final sentence before the page break tells DMs they can allow characters to use their existing proficiencies to use otherwise improvised weaponry. The example would be "since you're proficient with clubs, you're good to go with this table leg".
Then stats are suggested for improvised weaponry: 1d4. This would also go for when Legolas stabs orcs in the eye with his arrows. Finally the damage and range of "improvised thrown objects" are discussed.
Nowhere can you arrive at the conclusion "now I'm proficient with everything".
Normally when you pick up a table leg (or dead goblin ) you would be considered not proficient, and do d4 damage.
The DM could rule the table leg acts like a club, meaning it's a light weapon dealing bludgeoning damage. Complete with properties and all (in this case "light"). Then again, he could choose not to.
The DM could also rule the table leg IS a club, meaning you get your proficiency bonus (as well as any rider feature of using weaponry you're proficient with). Then again, he could choose not to.
What the Tavern Brawler does is, it ensures you get your proficency bonus when you pick up any random object.
Also, many DMs will choose not to be lenient with the two rulings above in general, in order to be exactly that for Tavern Brawlers. That is, any time a Tavern Brawler picks up a vaguely club:ish item, bam, it really is a club. But for anyone else, it isn't.
But it doesn't end there. Perhaps the Tavern Brawler can use a rope as a whip, a dead goblin as a greatclub, and a broken mirror as a scimitar? Complete with their proficiency bonus and all weapon properties and special rules!
When at the same time everybody else will simply get the same bog-standard d4 improvised weapon out of these items?
TL;DR: Sure, you could be generous and hand out most if not all the benefits of Tavern Brawler to anyone picking up a table leg.
But then again, you could choose not to.