An EICR should in theroy be only about the installation, the equipment is inspected with inspection and testing of in service electrical equipment, often called PAT testing although to be portable it either needs wheels or under 18 kg, however normally the lights are the odd one out and are included with the EICR.
Look in BS 7671 and we have
Electrical equipment (abbr: Equipment). Any item for such purposes as generation, conversion, transmission, distribution or utilisation of electrical energy. Such as machines, transformers. apparatus, measuring instruments, protective devices. wiring systems. accessories, appliances and luminaires.
Electrical installation (abbr: installation). An assembly of associated electrical equipment having co-ordinated characteristics to fulfil Specific purposes.
So in theroy equipment is part of the installation, and the building regulations say
“electrical installation” means fixed electrical cables or fixed electrical equipment located on the consumer’s side of the electricity supply meter;
So it is really up to the guy doing the EICR as to what he considered is part of the report.
What often causes a problem is "A circuit protective conductor shall be run to and terminated at each point in wiring and at each accessory except a lampholder having no exposed-conductive-parts and suspended from such a point." this started in 1966 with "D.6 At every lighting point an earthing terminal shall be provided and connected to the earth-continuity conductor of the final sub-circuit." in fact before that date back to 13th edition the exemption was only for "filament lamps" so since using LED which don't have a filament that earth is required, yet often left out when converting from extra low voltage to low voltage, and of course today needs RCD protection as well.
The other is not having the outer clamped within any junction box, many conversion kits have the primary insulation exposed, however the wording of the EICR is not does not comply with the current edition of BS 7671 that was dropped, it now say dangerous or potentially dangerous and lets face it, 230 volt is always potentially dangerous, so it is down to the whim of the inspector.
He can, and it has happened in Pembrokeshire where an electrician was taken to court and found guilty for not finding faults, however if the faults are listed but coded as a C3 it would be harder to say he was at fault. However it does mean electrician tend to list thinks which may by others not be considered as part of the EICR.
However it is an electrical report, not a fire report, and electricians also need to be careful to keep within their remit, so missing smoke alarms can't really fail an EICR but those which are smashed could, but being out of date is not really any thing to do with an EICR, the problem is to test a smoke alarm one needs a smoke generator, and I don't want to carry one of those around, so better to keep within my remit, and not refer to items outside the remit.
The same applies to other trades and professions, if some one does a house buyers report and they refer to any electrical system, then it could be seen as an EICR, so they need to be careful and state it is not an EICR, the same goes for electricians referring to things outside their remit.
One problem is clearly the boiler is fixed, it is not portable or moveable, but often one needs to be gas safe to remove the covers, so to follow the building regulations definition opens up a can of worms, which any electrician with some sense wants to avoid. So I state clearly only the insulation is part of this report, for equipment see the inspection and testing of in service electrical equipment.
But I have seen codes given to out of date smoke alarms, and too many items plugged into a socket, so not every inspector does that.