Plucking a number randomly from a real-world point-in-time snapshot of https://bitcoinfees.earn.com/, I see a suggestion of ~150 satoshis/byte, so for your example, transaction fees for an ideal/max size block would be 600 million satoshis = 6 BTC, which roughly is about the same as the block reward.

Needing to roughly double the status quo transaction fees to make up for lack of the block reward in order to provide equivalent security, doesn't seem ridiculous to me at all. And this is the worst case scenario (i.e. the reward will go from 6.25 to 0 slowly, but it can't go negative).

Where does 4 MB come from?

The average block size right now is 1.2 MB (the 0.2 MB because of SegWit). Assuming SegWit adoption increases to 100%, we get 1.6 MB.

The average fee on a transaction would need to rise $7.47 to match the post-halving's new, lower, security budget.

The average value of a transaction would need to double to make an average transaction fee of $14 (the current average fee of $6.50 + an increase of $7.50 to cover the loss of the security subsidy) economical.

But the doubling of value flows would make the current $security budget less adequate, so even less suitable for reserve currency usage.

And if the price increases, as Bitcoin investors hope it will, value flows would increase further, requiring an even larger security budget and average transaction fee.

At some point's further utilization and appreciation will be arrested by the diseconomies of scale caused by rising fees.