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I have been using the DMG spell point system since the DMG first came out. I understand your issues with not liking tables, and frankly I don't see a big reason why you couldn't just interpolate a simple formula and use that instead. It's already a fairly linear progression. One formula that comes fairly close is: spell points = 4 * LEVEL ^ (1 + LEVEL/100), rounded to the nearest integer. At level 1 this gives you 4 spell points; at level 5 you have 22 spell points; at level 11 you have 57 spell points; and by level 20 you have 146. Those numbers are all reasonably close to the DMG numbers (4, 27, 73, 133) although somewhat underpowered at low levels--they don't quite catch up to the DMG numbers until level 16, except for an anomaly at level 2 and a smaller anomaly at level 4. But they do remain within 2 levels of DMG numbers at all times.
I have been using the DMG spell point system since the DMG first came out. I understand your issues with not liking tables, and frankly I don't see a big reason why you couldn't just interpolate a simple formula and use that instead. It's already a fairly linear progression. One formula that comes fairly close is: spell points = 4 * LEVEL ^ (1 + LEVEL/100), rounded to the nearest integer. At level 1 this gives you 4 spell points; at level 5 you have 22 spell points; at level 11 you have 57 spell points; and by level 20 you have 146. Those numbers are all reasonably close to the DMG numbers (4, 27, 73, 133) although somewhat underpowered at low levels--they don't quite catch up to the DMG numbers until level 16, except for an anomaly at level 2 and a smaller anomaly at level 4. But they do remain within 2 levels of DMG numbers at all times.
Spell points by level:
Level 1 (DMG) 4 (formula) 4
Level 2 (DMG) 6 (formula) 8
Level 3 (DMG) 14 (formula) 12
Level 4 (DMG) 17 (formula) 17
Level 5 (DMG) 27 (formula) 22
Level 6 (DMG) 32 (formula) 27
Level 7 (DMG) 38 (formula) 32
Level 8 (DMG) 44 (formula) 38
Level 9 (DMG) 57 (formula) 44
Level 10 (DMG) 64 (formula) 50
Level 11 (DMG) 73 (formula) 58
Level 12 (DMG) 73 (formula) 65
Level 13 (DMG) 83 (formula) 73
Level 14 (DMG) 83 (formula) 81
Level 15 (DMG) 94 (formula) 91
Level 16 (DMG) 94 (formula) 100
Level 17 (DMG) 107 (formula) 110
Level 18 (DMG) 114 (formula) 121
Level 19 (DMG) 123 (formula) 133
Level 20 (DMG) 133 (formula) 146
Furthermore, I doubt the missing spell points would be all that sorely missed, since spell points systems give greater flexibility and there is less pressure to conserve some of every type of slot. A regular PHB 9th level wizard with only a 3rd level slot and two 1st level slot remaining would be quite nervous; but a spell point wizard with 9 spell points left is likely is be relatively cool and collected because he can still utilize any of his memorized spells and still have power a 1st level spell like Shield or Expeditious Retreat for emergencies. If you gave me a choice between running a spell point wizard under this formula or a PHB spell slot wizard, I'd take spell points every time.
My opinions on the 6th+ level slot issue are mostly theorycraft, because I've only played characters at those level in one-shots. IMO the biggest impact of that rule is that it makes multiclassing more attractive; since you can't get multiple 6th+ slots per day anyway, and you already have plenty of spell points, you might as well consider investing two levels in Rogue or Fighter or Warlock or something somewhere along the line instead of sticking with pure spellcaster classes.
Aesthetically I don't like the 6th+ limitation because it prevents it from being a real spell point system; it's actually a hybrid spell slot/spell point system because you still have to keep track of slots 6, 7, 8, and 9. But I don't have an elegant solution either, because 5E does clearly intend to keep a lid on level 6+ spells in a way that it doesn't for spell levels 1-5. (E.g. Arcane Recovery doesn't work with them, Sorcerers can't create them from sorcery points, etc.) If you held a knife to my throat and made me come up with a solution now I would simply increase the cost exponentially after level 5 and drop the 1/day restriction: spells over level 7 cost (14 * 1.4^(LEVEL - 5)) spell points, rounded to the nearest number.
Level 6: 20 spell points
Level 7: 27 spell points
Level 8: 38 spell points
Level 9: 54 spell points
Only the mightiest wizards could ever dream of casting multiple high-level spells in a day, and doing so would drain them utterly. That seems like it would maintain the flavor of 6th+ level spells in 5E: they're rare and significant.
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