SIPP Tax Relief

Hello, I keep thinking I understand this and then suddenly something doesn't make sense. I'm looking at using a SIPP instead of salary sacrifice. At first I thought this would give me more money in my pocket but it seems like actually I just lose out. Let's say I earn £80,000. I could salary sacrifice £10,000 and it would be like I earn £70,000 giving me a net income of £51158 (using an online calculator) and £10,000 in my pension. Or I could take the whole £80,000 salary and get a net income of £56958 (using same online calculator). I could then put the difference (£56958 - £51158) = £5800 into a SIPP. HMRC would auto add 25% to replace the 20% they took of adding £1450. Then I could claim another 25% to replace the other 20% they took off as a higher tax payer adding another £1450. This would make my SIPP worth £8700. It's now quite clear that in both scenarios I'd take home £51158. But by using a SIPP I end up with £8700 in my pension instead of £10000 in my pension.... What am I getting wrong?

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