Wouldn't it be a great idea if they spent those periodic burns on buying and holding bitcoin instead?
No, because this is not real "money", it's only numbers.
They have full control over their supply, so they can create coins out of thin air. As long as it sits idle and they don't put it into circulation, this is only a number in their database (only that it can be seen publicly because it's on a blockchain). But as long as they offer it on the market, they need it to be backed with assets, and demand has to exist for it.
So these burns only indicate that there is less demand for the stablecoin. And if they burn it, they need less assets to back it, which is better for their efficiency.
Buying Bitcoin instead would mean that they put it into circulation. This means they have to back it. And the stablecoins don't disappear when they buy BTC: they change ownership. In the case of USDT for example this has the effect that the USDT side of the USDT/BTC order book becomes thicker. A single BTC buy would not have a big effect, but in the long run, that would lead to a lower price for the stablecoin (measured in BTC) and thus increase the danger of a de-peg.
They thus could do this only if there is a demand surplus coming from BTC, i.e. many Bitcoiners trying to sell their BTC for the stablecoin.
Does not carrying out those periodic burns has any significant economic impacts or effects on crypto? Like the risk of stable coin inflation that could lead to depegging from the US dollars?
It's exactly the other way around: if they didn't burn and instead retain stablecoins in circulation which have no demand, then this could have a negative effect and even a depeg risk in the long term, as explained above.
Said simply: these stablecoins are not "needed" at that time. So they can burn them and liberate assets they hold to back them.
There could be a psychologic effect if for example USDT was burning and USDC was not: this could indicate there's less demand for USDT than for USDC and create fear among USDT holders. But that difference, I assume, has to be enormous to really put the USDT peg in danger.