An ordinary sparkler does not generate enough heat to reliably bootstrap a thermite reaction. It will burn the aluminum component but a thermite reaction is a completely different animal.
Typical thermite bootstraps are three stage for the simple reason that chemistry that is easy to ignite usually does not generate enough thermal power to bootstrap a thermite reaction. A sparkler has a composition that is very similar to a primary stage, a mixture of oxidizer and organics plus a bit of metal for better thermal power (or sparkles, in the case of a sparkler). This is used to ignite the booster stage, which does deliver sufficient thermal power to bootstrap a thermite reaction but is difficult to ignite directly because it is essentially inert anywhere close to room temperature. Boosters are typically direct metal oxidation reactions e.g. aluminum and sulfur.
Useful thermite also tends to be fairly coarse mesh size, which makes it more difficult to ignite. You can trigger a thermite reaction with a fine mesh thermite mixture but that will mostly just give you sunburn and blind you for a day -- typically you want a controlled burn.
Typical thermite bootstraps are three stage for the simple reason that chemistry that is easy to ignite usually does not generate enough thermal power to bootstrap a thermite reaction. A sparkler has a composition that is very similar to a primary stage, a mixture of oxidizer and organics plus a bit of metal for better thermal power (or sparkles, in the case of a sparkler). This is used to ignite the booster stage, which does deliver sufficient thermal power to bootstrap a thermite reaction but is difficult to ignite directly because it is essentially inert anywhere close to room temperature. Boosters are typically direct metal oxidation reactions e.g. aluminum and sulfur.
Useful thermite also tends to be fairly coarse mesh size, which makes it more difficult to ignite. You can trigger a thermite reaction with a fine mesh thermite mixture but that will mostly just give you sunburn and blind you for a day -- typically you want a controlled burn.