It's worth referring back to these answers which may help to answer your question:

1. u/Agrippa911's answer on why the US Army didn't switch to the BAR during the Korean war.
2. This thread on whether the firepower boost the M1 provided (compared to others' bolt-action service rifles) was of great benefit in the first place. The comments made apply equally to the greater firepower from giving everyone BARs.

My view of BARs:

1. They're heavy. 16lbs instead of c. 10lbs, and the greater rate of fire means carrying more heavy ammunition (especially if in magazines). This slows down the attack and is more suitable for a defensive war which the US wasn't fighting.
2. They're more complex and needed longer training to gain familarity and mastery than the M1.
3. They're really heavy.
4. The martial ethos of the US still espoused the individualist rugged marksman, able to pick of enemies at range. Overall doctrine also focused heavily on indirect fire (mortars, artillery, air support) to win the battle.
5. They're unsustainably heavy.
6. Prior to WWII Army Ordnance didn't want a protruding magazine on the general service rifle - they thought the magazines would be lost, and would permit dust and dirt to get in.
7. The 'walking fire' or 'marching fire' concept that the BAR was meant to fulfil never really showed much benefit; except in limited situations such as dense woodland.
8. They weigh a lot.

The Model 1918 BAR and M1 Garand were very different guns designed for very different roles. The Garand was designed from the ground up as an infantry rifle, but the BAR was at its inception an automatic rifle (an important distinction) that was adapted in several variants to be a light machinegun.

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The Automatic Rifle role the BAR was designed for at the end of WW1 was a peculiar concept that doesn't really seem practical in retrospect and didn't carry far beyond WW1. The BAR was supposed to be employed for semi-automatic fire from the hip as soldiers crossed no-man's land to suppress enemy defenses. Once soldiers reached the enemy trenches, they'd switch to fully-automatic fire for close-range combat. For this role, the BAR was very well designed. It was a heavy open-bolt design with a large detachable magazine that made it well-suited to putting out high volumes of fire while still being relatively mobile. While elements of the design made it less than ideal as a true light machinegun, it was arguably the ideal Automatic Rifle, however flawed that concept may have been.

But an automatic rifle like the BAR doesn't translate well to light machineguns, let alone something like an infantry rifle. The BAR was a very heavy gun, coming in at over 15 pounds in its lightest iteration. Its open-bolt operating mechanism was great for keeping the gun cool for rapid fire, but it hindered practical accuracy. And it was an expensive gun due to all the complicated machining required to produce it, meaning mass adoption as a standard infantry rifle wasn't going to be very practical. Even as a light machinegun, the BAR as adopted by the US Army was poorly suited to the role largely due to its lack of a quick-change barrel that limited its ability to perform sustained fire. Variants developed by FN in use in Belgium and Poland would add this (among other changes) and turn it into a very capable light machinegun, but this further added to the weight and cost of the gun.

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The M1 Garand, on the other hand, was excellently suited to what the US Army Ordnance Department was looking for. It was roughly half the weight of the BAR and only a little heavier than the 1903 Springfield. Its closed-bolt operating mechanism was ideal for practical accuracy, and its design was excellent for mass production. The magazine design was flush with the stock, which was a major design consideration intended to keep the magazine better protected against damage.