Why would a company buy and hold cryptocurrency as part of its strategy to accept payment in same?

As pointed out in the comments, holding BTC is not a prerequisite for accepting BTC payments.

As for the rationale, Tesla might try to position itself as a "though-leader" or "early adopter" in order to encourage the mainstream use and adoption of cryptocurrencies, which could help stabilize their volatility and increase liquidity.

I'm not aware of other large corporations that simultaneously announced the buying of cryptocurrencies and accepting them for payment.

From TSLA's 10-K filing (emphasis mine):

We hold and may acquire digital assets that may be subject to volatile market prices, impairment and unique risks of loss.

In January 2021, we updated our investment policy to provide us with more flexibility to further diversify and maximize returns on our cash that is not required to maintain adequate operating liquidity. As part of the policy, which was duly approved by the Audit Committee of our Board of Directors, we may invest a portion of such cash in certain alternative reserve assets including digital assets, gold bullion, gold exchange-traded funds and other assets as specified in the future. Thereafter, we invested an aggregate $1.50 billion in bitcoin under this policy and may acquire and hold digital assets from time to time or long-term. Moreover, we expect to begin accepting bitcoin as a form of payment for our products in the near future, subject to applicable laws and initially on a limited basis, which we may or may not liquidate upon receipt.

https://www.sec.gov/ix?doc=/Archives/edgar/data/1318605/000156459021004599/tsla-10k_20201231.htm