I think that your last paragraph really sums it up in a non-technical manner.
The stylus/cartridge should be perpendicular to the record groove. However, with a tonearm on a pivot, it will sweep across the record in an arc. The difference is called tracking error. The purpose of cartridge alignment is to minimize the tracking error. A fellow named Baerwald wrote a paper on tonearm geometry sixty or seventy years ago. His conclusion was that the cartridge should be aligned so that it is right on the perpendicular at 6.6 cm. and 12.1 cm. from the turntable spindle. This will minimize the tracking error and it is how cartridge alignment gauges are (should be) calibrated.
A linear tracking turntable eliminates this type of tracking error by having the whole tonearm slide across the turntable, rather than move on a pivot.
Also, think of a car going around a curve in the road. Some will hug the corner; some will rock outwards due to centrifugal force. Since the cartridge/tonearm is describing an arc, it is going around a curve constantly, except for the points 6.6 cm. and 12.1 cm. from the centre. A well designed cartridge and tonearm will ride the curve more easily, thereby keeping better contact with the record groove.
The stylus/cartridge should be perpendicular to the record groove. However, with a tonearm on a pivot, it will sweep across the record in an arc. The difference is called tracking error. The purpose of cartridge alignment is to minimize the tracking error. A fellow named Baerwald wrote a paper on tonearm geometry sixty or seventy years ago. His conclusion was that the cartridge should be aligned so that it is right on the perpendicular at 6.6 cm. and 12.1 cm. from the turntable spindle. This will minimize the tracking error and it is how cartridge alignment gauges are (should be) calibrated.
A linear tracking turntable eliminates this type of tracking error by having the whole tonearm slide across the turntable, rather than move on a pivot.
Also, think of a car going around a curve in the road. Some will hug the corner; some will rock outwards due to centrifugal force. Since the cartridge/tonearm is describing an arc, it is going around a curve constantly, except for the points 6.6 cm. and 12.1 cm. from the centre. A well designed cartridge and tonearm will ride the curve more easily, thereby keeping better contact with the record groove.