I haven’t done this but I believe you could instigate a DMA transfer via the 2MHz ‘tube’ interface and write the image directly into RAM. That would require additional hardware but no modifications to the machine itself.
Additionally you had full read/write and execute access on any other station's RAM (including video RAM) if you used assembly language. This is without any authentication required, so there was no security in that aspect.
For the ZX Spectrum:
Sorted by amount of non standard modern equipment needed (less to more):
A smartphone with SpeccyTape (IOS, unfortunately, now unmaintained and not available for 64 bit devices) or PlayZX (Android) and a stereo to mono cable.
TZXDuino / TAPDuino: hobbyst grade gadget (built and sold in several places) that essentially does the same as ...
This is a wiki answer, so please amend with additional solutions, or improve the ones below:
CPC Tape Software
Tape images are normally downloaded as a .cdt file, the same file format as the Spectrum .tzx tape format. Though these do not contain any sound data, they can be played back on an Android or iOS phone, using an app such as 'PlayZX' or 'Speccy Tape'....
Most of BBC BASIC's speed advantage came from Acorn's use of a 2 MHz 6502 with fast 4816A RAM chips. It's a good interpreter, but it's the hardware that makes it near-mythically fast.
To confirm this, one can run J. G. Harston's port of 6502 BBC BASIC for Commodore 64. This is essentially the Acorn BBC Micro's interpreter lightly patched to talk to KERNAL ...