An artificial constraint can't be the basis for organic fee pressure.
There is nothing 'artificial' about the transaction rate. It's just an operational parameter which defines how the system works and is no more 'artificial' than the 21m currency base, the 10min block frequency, or the POW algorithm. Changing this parameter will have pros and cons, just as would changing any number of other operational parameters.
Folks like me who wish to see the transaction rate rather severely limited simply value the aspects which are enhanced by having a low data rate. In my case I highly value the potential flexibility to adapt to certain types of attack (which we've not seen yet.)
Conversely, having a wide userbase for native Bitcoin itself is not very interesting, and in fact I consider it a negative. Most users add nothing toward infrastructure support even at our low data rate. Most people are not prepared technically to safegaurd their BTC and Bitcoin get's egg on it's face every time one of them gets ripped off, and it is an appallingly inferior solution for run-of-the-mill coffee purchases anyway compared to systems which were designed from the get-go to be real-time.
Organic fee pressure would exist on the basis of the increased block orphan risk with each added tx. In the long run, if those fees are not sufficient to pay for adequate security, I would expect miners to form a cartel to enforce some minimum fees. I could understand a cartel seeming like an artificial constraint as well, and in some senses it would be one; though having a different basis than a software hard-limit would give the nature of the constraint different properties. For instance, a mining cartel would be able to adjust their fee policy in real time if they so desired.
Ultimately I would like to get rid of the mining cartels themselves as mentioned in my last post above. There is some chance that that would happen to their detriment should they abuse their power which is probably the main reason it has not happened already. Block size has relatively little to do with it one way or another I don't guess.
Since I've not mentioned it for a while, note that mining never has the potential to be profitable in the long term whether the reward comes from coinbase or from fees or from some combination. The simple reason for this is that capacity will rapidly grow to take all of the excess. The higher the profitability, the stronger this differential which creates growth and makes the profitability point be hit that much sooner. The only solution is to consolidate and start monetizing business intelligence which will further squeeze out miners who are not of size to do so efficiently, but then we have a shitty PayPal-II and that ugly reality cannot be hidden forever. That really would open the door for distributed crypto-currency which adhered more to some of the original principles of Bitcoin and could make Bitcoin go extinct (and at that point I would hope for this outcome.)