I see what you mean!
I was thinking along the lines of agnatic succession from a common ancestor. Like the Saudi system - or at least as it once operated. You'd just go through this former monarch's sons until they were all dead. And then start on grandsons. If that makes sense.
Yes, it does; I did see the link with the Saudi system. It's a great system for those who prefer older monarchs. However, I wonder for how many generations it works to keep this pattern. Let's try to see how this would work if the British royal family would have started adopting this system with George V (but including the women as well; as that is the current British practice; and it would get queen Elizabeth on the throne at this point).
King George V (reigned until 1936)
First generation
1. King Edward VIII (b. 1894; reign 1936)
2. King George VI (Albert) (b. 1895; reign 1936 - 1952)
3. Queen Mary (b. 1897; reign 1952 - 1965)
4. King Henry (b. 1900; reign 1965 - 1974)
Second generation
5. King George VII (b. 1923; reign 1974 - 2011)
6. Queen Elizabeth II (b. 1926; reign 2011 - now)
Line to the throne:
(still second generation from oldest to youngest))
1. The Duke of Kent (b. 1935)
2. Princess Alexandra of Kent (b. 1936)
3. Prince Michael of Kent (b. 1942)
4. The Duke of Gloucester (b. 1944)
Third generation
5. The Prince of Wales (Nov 1948)
6. The Princess Royal (Aug 1950)
7. The Earl of Harewood (Oct 1950)
8. Henry Lascelles (May 1953)
9. The Hon. James Lascelles (Oct 1953)
10. The Hon. Jeremy Lascelles (Feb 1955)
11. The Duke of York (Feb 1960)
12. The Earl of Snowdon (Nov 1961)
13. Earl of St Andrew (June 1962)
14. James Ogilvy (Feb 1964)
15. The Earl of Wessex (March 1964)
16. Lady Helen Taylor (April 1964)
17. Lady Sarah Chatto (May 1964)
18. Marina Ogilvy (July 1966)
19. Lord Nicholas Windsor (July 1970)
20. Earl of Ulster (Oct 1974)
21. Lady Davina Lewis/Windsor (Nov 1977)
22. Lord Frederick Windsor (April 1979)
23. Lady Rose Gilman (March 1980)
24. Lady Gabriella Windsor (April 1981)
Fourth generation
25. Sophie Pearce (Oct 1973)
26. Rowan Lascelles (Nov 1977)
27. Peter Phillips (Nov 1977)
28. Viscount Lascelles (May 1980)
29. Zara Tindall (May 1981)
30. The Duke of Cambridge (June 1982)
31. Thomas Lascelles (Sept 1982)
32. The Hon. Edward Lascelles (Nov 1982)
33. The Duke of Sussex (Sept 1984)
34. Ellen Lascelles (Dec 1984)
35. Amy Lascelles (June 1986)
36. Princess Beatrice (of York) (Aug 1988)
37. Lord Downpatrick (Dec 1988)
38. Princess Eugenie (of York) (March 1990)
39. Zenouska Mowatt (May 1990)
40. Maximilian Lascelles (Dec 1991)
41. Lady Marina Windsor (Sept 1992)
42. Christian Mowatt (June 1993)
43. Columbus Taylor (Aug 1994)
44. Flora Vesterberg (Dec 1994)
45. Lady Amelia Windsor (Aug 1995)
46. Samuel Chatto (July 1996)
47. Alexander Ogilvy (Nov 1996)
48. Cassius Taylor (Dec 1996)
49. Arthur Chatto (Feb 1999)
50. Viscount Linley (July 1999)
51. Lady Margarita Armstrong-Jones (May 2002)
52. Eloise Taylor (March 2003)
53. Lady Louise Mountbatten-Windsor (Nov 2003)
54. Estella Taylor (Dec 2004)
55. Tallulah Lascelles (Nov 2005)
56. Lord Culloden (March 2007)
57. Albert Windsor (Sept 2007)
58. Viscount Severn (Dec 2007)
59. Leopold Windsor (Sept 2009)
60. Lady Cosima Windsor (May 2010)
61. Lila Gilman (May 2010)
62. Senna Lewis (June 2010)
63. Tane Lewis (May 2012)
64. Rufus Gilman (Oct 2012)
65. Maud Windsor (Aug 2013)
66. Louis Windsor (May 2014)
67. Isabella Windsor (Jan 2016)
Fifth generation
68. Savannah Phillips (Dec 2010)
69. Isla Phillips (March 2012)
70. Prince George of Cambridge (July 2013)
71. Mia Tindall (Jan 2014)
72. Princess Charlotte of Cambridge (May 2015)
73. Cloe Lascelles (2017)
74. Prince Louis of Cambridge (April 2018)
75. Lena Tindall (June 2018)
76. Ivy Lascelles (Oct 2018)
77. Archie Mountbatten-Windsor (May 2019)
78. Sebastian Lascelles (Aug 2020)
N.B. I only included children (and their descendants) born within marriage and not conceived while in a previous marriage.
UPDATED