So, when I approach my manager about this issue, is it reasonable to expect such a compromise?
Your boss cares about what you do on the job, not so much what you do on your own time. Commuting, taking place before and after work hours, is not on-the-job time, and so your boss doesn't care about it. If you lived far enough away that the average commute time for you was three hours, and you took the job, your boss wouldn't have any reason to extend any special benefits to you-- you accepted the job, including the commute you would have to make. That also includes the risk of rare, adverse events, like traffic jams.
That the traffic issues you are describing were totally out of your control is irrelevant-- your ethical (and contractual) obligations to your employer are apparently to work a set number of hours each day. It would be good if your employer cut you some slack on freak occurrences, but the business's function is to get specific work done in a specific way, not to suit your preferences or convenience. When those come into conflict, your boss is likely to prioritize the former.
Consider: if you were stricken by an illness, unexpectedly and without any ability to increase or reduce your risk of getting it, which left you physically able to work only 1 hour per day, would you expect your employer to pay you the same amount despite your reduced time in the office? It's equally "not your fault" in that case.
From what you've written your understanding of economics seems to be... nonstandard. For a variety of reasons (including, but not limited to, that) I would recommend that you not use it as the basis for your position when speaking with your manager. Further, your employer seems to have explicitly decided not to allow flexible scheduling of the sort that you're after. That will make a negotiation seeking exactly that difficult for you, regardless of any discussion of fairness or elasticities. But, if economics is on the table, let's look at some other distributional effects.
Being pseudo-salaried makes this more complicated, as you can't chop up the workday (you get paid the same either way), and so leaving early = less of what your employer wants and expects of you (which is to be on-site for a set number of hours each day).
But since the employer pays you the same amount either way, 100% of the benefit of your spending less time in the office accrues to you, and none to the employer. There is also no clearly analogous situation on the other side-- if you happened to have a really fast commute one day and got to work a half-hour early, would your employer get an additional 30 minutes of work from you "for free"? Even if I agreed with your take on elasticities and distributions of economic burden, these features would still make your position unattractive to me (if I were your manager).
If you do talk to your manager about this, I would focus exclusively on the rarity of your being late, the lack of impact on the work you get done, and the disruptiveness staying late would have on your life. I would also set an "upper bound" that would reassure your boss that you won't take advantage of their agreeing to this (something like, if you're late 4 times in a year then the deal is off).
When everything else that the company wants gets done, and you are complying with the policy 99.9% of the time, mutually-agreed to protections against your taking advantage of the situation exist, and the actual loss to the company for accommodating you here is therefore minimal, it's more likely that you'll get whatever flexibility your boss might be able to offer.