First you have to explain in detail the meaning of BTC being legally accepted, accepted as an investment vehicle or as a means of payment? If it is accepted as an investment vehicle or digital asset, maybe this makes sense and in the future there will be regulations governing this issue. but if it is accepted as a means of payment, this seems impossible because it is impossible for there to be any other legal means of payment other than fiat currency.
Bitcoins cannot be officially accepted as a mode of payment. This is because Bitcoins are limited or fixed in number. Hence this can consider as a finite asset. Yes you can trade the coins for something in return, but cannot use it as a mode of payment.
Now regarding OP’s concern, he is asking if it’s legalised as an asset, and have governments support, then what will be the scenario? According to me, it will lead to increase in demand to buy the coins and hence the price will go up.