Not true. All scanners sold in the US (except government versions) have cellular frequencies blocked out, and very few scanners on the market have "continuous band coverage" in general. Almost every scanner on the market has several frequency ranges/bands within their overall "range" that cannot be received. Only the higher-end scanners can receive "digital transmissions", most scanner models are analog-only.
There are a couple "wide-range receivers" by Icom and AOR that have true continuous band coverage. While these models do "scan" (slowly), they are generally not considered to be "scanners" as we know them. Also, these models cannot follow a trunked system or decode P25 digital.
Also not true, there are several non-encrypted system types that cannot be received by any scanner currently on the market. Systems such as MotoTRBO, ProVoice, and TETRA cannot be monitored by any scanner itself. Motorola's X2-TDMA can be monitored by only 1 scanner model, (the GRE PSR800).
Again, not true. With the exception of vintage crystal scanners and very early digital models, all "modern" scanners have a search feature which can detect "new" local [active] frequencies.
Beyond the simple search feature, Uniden DMA scanners have a proximity-based feature called "close call" which will detect strong signals nearby (and if enabled, it can auto-store the frequencies it finds). GRE models have a similar proximity feature called "Signal Stalker".