Why can't we geminate affricates in sentences when talking?

The main reason is that gemination does not take place in complex segments. 'Affricates' are complex segments; they start off as plosives, but finish as fricatives (they have two manners of articulation).

Or because affricates are composed of two different kinds of sounds (plosives + fricatives).
We usually geminate two similar sounds when they're next to each other:

• Bad day -> [bæd̚.deɪ]
• This sin -> [ðɪsːɪn] etc.

The /d/ and /s/ can be geminated because we don't have any complex segments here.

However, when two affricates come next to each other, we get four different kinds of sounds:

• Orange juice -> [ɒɹɪnd͡ʒ.d͡ʒuːs]: [d ʒ d ʒ]

• Which chair -> [wɪt͡ʃ.t͡ʃeə]: [t ʃ t ʃ]

In case of 'continuants', the geminate is just a longer version of the continuant.

• His zone -> [hɪz:əʊn]
• Solely -> [səʊlːi]

However, 'stops' don't do the same because they're obstruents. Their gemination often results in an 'unreleased stop' followed by a released one:

• Lamp post -> [læmp̚pʰəʊst] (not [læmppʰəʊst]).
• Bad day -> [bæd̚deɪ]

Affricates can be thought of as 'stops', but with a fricative release, so if the first affricate is unreleased ([t̚] or [d̚]), their geminates are supposed to be pronounced (not how they're pronounced):

• [t̚t͡ʃ] and
• [d̚d͡ʒ]

that's why they can be confusing.

From Sounds of the Worlds Languages (1st Edition) by Peter Ladefoged:

Geminate affricates are very clearly different from an affricate sequence, since the sequence has two stop and two frication portions, while a geminate affricate has a long stop closure followed by one fricative portion.

But he doesn't explain why they don't occur in English.