Hey
Is the maximum load increase too slow? Depends on where you compare it.
Compare it to westside or some other strength-training routine, then yeah, you can say it is too slow. If you simply want to increase your strength (1RM), then HST may not be your best option.
But if you are after hypertrophy, is this a problem, as your friend pointed out?
Not at all. Hypertrophy does not require using your maximum load all the time, or increasing it all the time before you experience growth. What does hypertrophy require?
In broad strokes and simplified, you can say hypertrophy starts when a significant strain is registered in the strain-sensing pathways of the muscles. How significant this needs to be depends on your level of conditioning at that time (possibly a combination of neural efficiency for fiber recruitment and amount of connective tissue present; this also means it DOESN'T have to be your super-heavy max load at all). After such a bout, satellite cells are differentiated, but not necessarily proliferated (you need both differentiation and proliferation to get growth), satellite cell proliferation requires a more chronic application of the stimulus (hence we train more frequently than just once a week, or only when we have the time). Mechanical stress (that is transmitted to the sarcolemma and sarcomeres) triggers focal adhesion kinases which start signaling events that lead to an increase in protein synthesis. You would already be growing as those events keep happening, but if oxidative/hypoxic stress is also present, you can grow faster. Bottom line, all these result in hypertrophy. Nowhere in the requirements of hypertrophy does it state "must lift max load most often or increase max load rapidly to initiate growth".
Why not max loads all the time? Because we SD, and our conditioning lowers, allowing lower weights to be effective again. So we start with a submaximal weight, we use those weights to get all the hypetrophy we can from them then move on... so we only end up using our max weights at the end of the cycle, not because max weights are magical but because that's the amount of load we need by that time to realistically be able to create a significant strain without frying your CNS (or simply overfatiguing yourself and draining you completely) due to tremendous numbers of reps. As that max load becomes ineffective, we simply SD again (of course, negatives if you wish, but you still have to SD eventually) to lower the conditioning and make lower weights effective again. Of course, as we grow bigger, we get stronger, and your 1RM will keep on increasing, even though you spend a lot of your time lifting lower weights.
If you take those things in mind, you'll realize working with your max weights isn't a necessity, or rapidly increasing your 1RM for that matter, in order to experience rapid hypertrophy. If your friend understands that and still thinks HST has a problem, perhaps he is after strength instead of size.