THIS REGARDS WHY YOU NEED THE TRANSITION PIECES, BOTH THE OBVIOUS REASONS AND ONE THAT IS NOT SO OBVIOUS.
I wanted to add this earlier but realized it would be difficult if not impossible to explain without this diagram and I both had to go run errands and take a while to draw this. Here is the diagram, I discuss it further below;
When I first got into 'Streets, I thought the only reason that you needed transition pieces was for the problem shown in the top diagram above. Without a transition piece in place (as shown), a vehicle exiting a curve was likely to have its flanges hit the edge of the narrowed grove at the head of the straight, either derailing or at least making an unwelcome bang and wobble. I reasoned that I did not need a transition piece when the vehcile was going the other direction from that shown -if the vehicle in the top diagram was existing the straight and just entering the curve, there would be no edge for the flange to hit.
Since I was making two-lane roads everywhere, with traffic flow restricted to one direction on each side, I thought I could leave out half of the tranistion pieces: cars in each lane would never be going back the other way. I only needed transition pieces everytime traffic in a lane exiting a curve into a straight, but not when it left a straight into a curve. When I ran out of transition pieces while building my roads, I left them out in those cases.
And for a while, it worked, at least with the vintage truck and the panel van and the short little school-bus vehciles. But when I first got the big UPS-like panel vans, which have the longest wheelbase of any stock 'Streets vehicle, I discuvered the second reason you need a transition piece, and why you need one on both the entry and exit of every curve. The bottom diagram above shows a vehicle leaving the straight into a curve on a section without a transition piece. The front axle flanges did not hit an edge because there was not one for them to hit when leaving a straight into a curve, BUT, a split second later, as the vehicle is well into the turn and only the rear axle is still in the narrow straight-section's grove, there is a moment where that groove is not quite wide enough to accomodate the flange at the angle the vehicle's geometry wants to pivot the whole vehicle at that point. The wheel flange has no choice but to work itself up halfway, or more, out of the groove and off the rail.
Among 'Streets vehciles, this particular (lower diagram) problem only seems to happen to the UPS-like panel van. The other vehicles can get by without the transition piece when going into a curve. However, for vehicles like trolleys or bashed "Streets vehciles that that have fixed (non-pivoting) axles, and long wheelbases and particularly if large diameter wheels compared to other 'Streets vehicles - they need it too.
Thus, my recommendation anytime is to use them both going into and leaving.
Interestingly, an example of not following the instructions and this reocmmendation is the Photo on the cover of QGR run 260 (the last Christmas issue). If you carefully look at the 'Streets road in the background (just above the trolley) you can clearly see a curve to straight without the transition piece in place. I don't know whether this scene was just staged or if any attempt was made to actually run the trolley. However, given it has pivoting trucks and rather small wheels, this particular trolley will probably run through that point in either direction okay, but a little roughly with a bang on occasion. A transition piece is called for in the 'streets instructions and recommended (the trolley would run much smoother there) - and it is required if you are running a trolley with non-pivoting axles, such as the Lionel trolley.
For this reason I now always put in a transition piece as the instructions call for - going into and out of every curve.