It's not a matter of a company choosing to allow an 83(b) election. It's a personal tax election that you make by mailing a filing in to the IRS and you can do it without the company's involvement or permision.

The problem is that 83(b) elections just aren't applicable unless (i) you own stock, not options, and (ii) that stock is subject to vesting.

Longer explanation: When you buy something, if you are paying less than the fair market value for that thing, then the spread is taxable income to you. Typically this spread is calculated at the time of the sale, so if you're buying shares at $0.0001 per share and they are currently worth $0.0001 per share, you'd think there would be no problem. But the IRS says that if shares are subject to vesting then the spread is actually calculated at the time that the shares vest. So a common case would be that you buy shares now for $0.0001/share, next year you hit your cliff and a bunch of shares vest, and at that point the price has gone up to say $0.001/share, and you would then owe taxes on the difference between $0.0001 and $0.001 per share. The 83(b) election gets you out of this trouble by letting you say at the very beginning that you want to be taxed on all shares up front, so the spread is calculated on day one, and is 0, and there's no tax liability.

So if you own shares and they are subject to vesting, either by a purchase of restricted stock or an option exercise, then yeah, make an 83(b) election and you can do that with or without the company's permission. But if you just own an option that you haven't yet exercised then an 83(b) election just doesn't apply and it's not something the company chooses to allow or not allow.