Do modern jet engines need igniters?
Jet fuel will not self-ignite when starting a modern turbine engine.
This article from the WingMag Aviation Magazine says:

As the temperature isn’t quite sufficient to initiate self-ignition (the autoignition temperature of aviation fuel is around 220 degrees Celsius), spark plugs are arranged around the combustion chamber. They generate a spark that ignites the air-fuel mixture and the turbine now drives the fan and compressor through a shaft, as described above. The exhaust gas temperatures begin to rise and the engine will now keep “running” as long as there is a supply of aviation fuel. The igniters are switched off by the FADEC once the exhaust gas reaches a certain temperature because they are no longer needed.

Once the engine is running at a sufficiently high speed, the autoignition temperature can be sustained (same article):

[The fuel] is injected into the combustion chamber through several “fuel nozzles” where it can self-ignite and continue to run if the temperatures are sufficiently high.

See also How is combustion flame maintained in the combustion chamber after igniters are switched off?
Igniters are not only needed for a cold start. They are also used in case of an engine flameout. From the Boeing 747-8 FCOM (7.20.8 - Engine System Description, emphasis mine):

Auto-Relight
An auto-relight capability is provided for flameout and rollback protection.
Whenever the EEC detects an engine flamout or rollback, both igniters are
activated. A flameout is detected when a rapid decrease in N2 occurs. A rollback
is detected when N2 falls below idle RPM or compressor pressure falls below idle
minimums.

Note that this is for a modern jet engine, the General Electric GEnx.