In 1967, a magazine article, cited a few times in the decade afterwards, said:
The cursor (entry marker) identifies the next display position to be entered. The cursor continually blinks three to five times per second, which permits quick visual location by the operator. — F. H. Reagan Jr. (February 1967). "Viewing the CRT Display Terminals". Data Processing Magazine. pp. 32–37.
It was talking about the Datanet-760 Keyboard/Display System from General Electric, which came out in 1965. A 1966 report from Auerbach says the same thing:
The cursor continually blinks 3 to 5 times per second, which permits quick visual location by the operator. — "GE DATANET-760 KEYBOARD/DISPLAY SUBSYSTEM". Auerbach Data Communications Reports. November 1966. p. 6321:06
cursor is nondestructive and blinks continually 3 to 5 times a second to aid operator visibility; — "GE DATANET-760 KEYBOARD/DISPLAY SUBSYSTEM". Auerbach Data Communications Reports. November 1966. p. 6321:09
(Note to readers of these Auerbach Data Communications Reports on-line: The reports were issued over a period of several years, and the document that you see all of these decades later is an accumulation of looseleaf inserts. The actual date of each item is in MM/YY format in the corners of the pages.)
This gives you one of the earliest terminals that had a blinking cursor, and the reason why it had a blinking cursor. Since both Auerbach and M. Reagan used exactly the same sentence, I presume that this originated with General Electric doco and can be viewed as GE's own rationale for this feature.
The GE user manual, the Auerbach report, and the magazine article all show prior art to the widely claimed invention of the blinking cursor by Charles A. Kiesling at Sperry Rand, whose patent was filed later, in August 1967. Whether this, in its turn, is the invention of the blinking cursor, and who exactly at GE did this, I cannot tell you.
You are rather assuming that the cursor has one shape. In fact, it hasn't. At the time, as alluded to in the Sperry patent, the shapes of cursors were a lot more varied than they are now in GUI terminal emulator programs. Terminals used horizontal lines, vertical lines, rotated "L" shapes, underscores, underscores+overlines, and blocks. The innovation in the middle 1960s is specifically a cursor that blinks.
As you can see from the report, the Datanet-760 was one of several terminals where the text could be made to blink, also. Blinking was a way to draw attention to more than just the cursor.
Ironically, it was the microcomputer revolution that narrowed the shapes down. Microcomputers employed off-the-shelf VDAC/VTLC/CRTC parts that, by the 1970s, had mostly settled on cursors formed by inclusive/exclusive-ORing the character ROM output, under the control of a counter that was clocked by the vertical synch and logic to select which scan lines this applied to. The start and end scan lines, the blink cycle, and whether blinking was enabled, were all in programmable hardware registers.
This gave us a lot of equipment with these semantics, which is what you see in emulator programs, emulating these things on GUIs in software, today. The GUI programs have within the past couple of decades added things such as vertical line and box cursors which the 1970s and 1980s hardware did not have but that the more widely varied 1960s in some cases did have.
Interestingly, they have also reversed direction on blinking, with people changing terminal emulators to default to non-blinking cursors. This is because these are not hardware cursors, implemented as OR circuitry. They aren't even sprites. They are purely rasterized shapes in GUI window display memory, which a processor has to wake up and re-draw at every blink state change, continually.