How would any of that make payment in shares beneficial compared to cash payment?

$12B cash appears to be all they have available. They can't pay more cash.

https://www.marketwatch.com/investing/stock/nvda/financials/...

Their only other option would be taking on debt.

Right, so Nvidia with their A2 rating and their solid balance sheet in a rock bottom interest rate environment still found it favourable to purchase Arm with newly issued shares.

That's telling us something about what they think about their share valuation right now.

That's not how interest works. "Low rate environments" are low rate because debt is less attractive than in a high rate environment. Debt isn't automatically preferable when interest rates are low - if it were, rates would rise. There's no free lunch.

All it tells you is that they think it's preferable to taking on debt, which in some sense is the position you always start from. Debt has a deadweight cost that you have to overcome.

But we can test your theory. You're saying they thought their shares were overvalued. The market's reaction was the opposite - announcing the deal bumped their share price 7.5%.

Perhaps there are tax implications?