Why is there a period after a royal title?

According to the 1949 Bibliographical description and cataloguing by John Duncan Cowley:

The earliest printers used roman numerals more often than arabic and usually divided a long numeral by means of stops, thus:

M.ccccc.xvij.
M. v. C. xxvij.
M | CCCCC. | XLII.
M. D. xliii

They also habitually printed a stop before as well as after roman numerals and occasionally adopted the same practice with arabic numbers, e.g.

The price of the whole boke (.xl.s.) whych boke conteynyth .iii. grete volumes.
... die .x. Februarii.
. . . the .xxii. day of Deceber in the .xix | yere of the reyngne of oure so | uerayne lorde kinge Henry | the .viii. |
. . . Anno .1568.

Even when a contracted word precedes the numeral, a stop between the two as often as not belongs to the numeral:

. . . Anno Dom .M.D. xv.

Sometimes the end of a line serves instead of a preceding or succeeding stop, but not always; in fact the preceding stop may be separated from the numeral by the line-ending, e.g.

. . . al .xviii. an du | tresuictorieux et so | ueraigne roy | Henry le. | viii.|

Check the book for an example from 1510 that illustrates how careful you must be reading these periods; if you're not careful you may read 1st April 1517 instead of 26th March 1510.

Perhaps due to these complications, these practices were simplified over time. For example, an 1897 American Printer and Lithographer says:

It is also proper to use the period after Roman numerals, where the " th " is understood, as " Charles XII. of Sweden," rendered in reading aloud "Charles the Twelfth, of Sweden." The rule is an arbitrary one, since it is not carried out in the case of the Arabic numerals, as, for instance, Feb. 24 would never appear with a period after ...

This advice changed around 1900 and by 1920 A Concise Manual of Style says:

Period. Omit period after roman numerals when used in such cases as Chapter I, Henry IV, Part VIII, etc.