This is normal. The algorithm that I wrote for MechJeb in KSP that uses Runge-Kutta and Calculus of Variations for vacuum-optimal-and-precise guidance still shows this behavior.
The problem is with high TWR rockets that have a short burntime to insertion (generally something like a Titan II or earlier rocketry). The best way that I can think of to explain the issue is that while MOST of the problem with getting to orbit is actually going horizontal very, very fast, you cannot neglect the vertical problem.
To hit a circular insertion orbit of something like 185km altitude you do need to acquire a fairly substantial vertical velocity and then lose it all pretty quickly. If you have enough burntime-to-orbit then you can rely more on gravity to do the work of slowing down your vertical velocity as you approach your insertion point. If you don't have enough time for gravity to act, though, you're going to have to do that work yourself and the rocket will point somewhat down to kill the vertical velocity it needed to gain in order to achieve the target insertion altitude.
There is no inefficiency or suboptimality in this, it is the optimal solution to the problem that you've given it, but one of the constraints you've given the optimizer is the parameters of your rocket and a single-burn-to-orbit, which constrains the burntime.
One way to fix this is what the shuttle does which is to include a coast and then a small insertion burn on OMS thrusters. That allows gravity time to act during the coast to kill the vertical velocity. But PEG cannot compute the optimal time of that coast, and you need an optimization model with aerodynamics to really solve it properly and avoid overly long coasts which either pass through the surface of the Earth or spend too much time going too fast too low which cause the rocket to burn up. But constraining the coast time to something around 600-1200 should produce reasonable results assuming your initial pitch program gets you out of the atmosphere reasonably enough.
You can't do that for e.g. a two stage Titan 2 though since the upper stage is not relightable and positioning the coast in between the two stages is very much not the optimal coast. You want to coast on a "transfer orbit" which is something like an elliptical orbit with the apoapsis at your insertion point and the periapsis something around 0km. You want to do an insertion burn of 300-1,000 m/s or so, which means you want to coast only after you've done some 8,000-ish m/s or more of work with the boosters. With a Titan 2 you get something more like 4,500 m/s out of the booster and 4,500 m/s out of the upper stage and you're not really going fast enough at stage separation. You can still use a coast there to more optimally hit some insertion targets (assuming an ahistorical Titan 2 which has some kind of attitude control added for the coast phase), but it still won't "look optimal" and will burn down at insertion.
Of course you can put a payload on the Titan 2, sufficient to make it so that the rocket only delivers around ~8,000 m/s to the payload, then separate and coast and do the insertion burn on the payload stage. Then you shouldn't see the payload stage burning down (much). Due to linear tangent steering though if your vgo is horizontal you will want to "sweep" from slightly over to slightly below horizontal.
TL;DR: The problem is [mostly] caused by needing to go up very quickly and then arrest your vertical velocity faster than gravity can help you out because of a short time-to-insertion.